diff --git a/polymer/eduke32/build/include/build.h b/polymer/eduke32/build/include/build.h
index 24d18d631..5021c592e 100644
--- a/polymer/eduke32/build/include/build.h
+++ b/polymer/eduke32/build/include/build.h
@@ -77,8 +77,10 @@ enum rendmode_t {
 #define MAXPLAYERS 16
 #define MAXBASEPALS 8
 #define MAXPALOOKUPS 256
+// Maximum number of defined multi-pskies:
 #define MAXPSKYMULTIS 8
-#define MAXPSKYTILES 256
+// Maximum number of component tiles in a multi-psky:
+#define MAXPSKYTILES 8
 #define MAXSPRITESONSCREEN 4096
 #define MAXUNIQHUDID 256 //Extra slots so HUD models can store animation state without messing game sprites
 
@@ -740,21 +742,39 @@ EXTERN uint8_t palette[768];
 EXTERN int16_t numshades;
 EXTERN char *palookup[MAXPALOOKUPS];
 EXTERN uint8_t **basepaltableptr;
-EXTERN char parallaxtype, showinvisibility;
-EXTERN int32_t parallaxyoffs, parallaxyscale;
+EXTERN char showinvisibility;
 EXTERN int32_t g_visibility, parallaxvisibility;
 EXTERN int32_t g_rotatespriteNoWidescreen;
 
 EXTERN int32_t windowx1, windowy1, windowx2, windowy2;
 EXTERN int16_t startumost[MAXXDIM], startdmost[MAXXDIM];
 
-// original multi-psky handling (only one per map)
-EXTERN int16_t pskyoff[MAXPSKYTILES], pskybits;
-// new multi-psky -- up to MAXPSKYMULTIS
-EXTERN int16_t pskynummultis;
-EXTERN int32_t pskymultiyscale[MAXPSKYMULTIS];
-EXTERN int16_t pskymultilist[MAXPSKYMULTIS], pskymultibits[MAXPSKYMULTIS];
-EXTERN int16_t pskymultioff[MAXPSKYMULTIS][MAXPSKYTILES];
+// The maximum tile offset ever used in any tiled parallaxed multi-sky.
+#define PSKYOFF_MAX 4
+
+typedef struct {
+    // The proportion at which looking up/down affects the apparent 'horiz' of
+    // a parallaxed sky, scaled by 65536 (so, a value of 65536 makes it align
+    // with the drawn surrounding scene):
+    int32_t horizfrac;
+
+    // The texel index offset in the y direction of a parallaxed sky:
+    // XXX: currently always 0.
+    int32_t yoffs;
+
+    int8_t lognumtiles;  // 1<<bits: number of tiles in multi-sky
+    int8_t tileofs[MAXPSKYTILES];  // for 0 <= j < (1<<bits): tile offset relative to basetile
+} psky_t;
+
+// Original multi-psky handling, only one per map:
+EXTERN psky_t g_psky;
+// New multi-psky -- up to MAXPSKYMULTIS (effectively constant after initialization):
+EXTERN int32_t pskynummultis;
+EXTERN psky_t multipsky[MAXPSKYMULTIS];
+// Mapping of multi-sky index to base sky tile number:
+EXTERN int32_t multipskytile[MAXPSKYMULTIS];
+
+EXTERN char parallaxtype;
 
 // last sprite in the freelist, that is the spritenum for which
 //   .statnum==MAXSTATUS && nextspritestat[spritenum]==-1
diff --git a/polymer/eduke32/build/include/common.h b/polymer/eduke32/build/include/common.h
index 89efb1d1b..ead031e30 100644
--- a/polymer/eduke32/build/include/common.h
+++ b/polymer/eduke32/build/include/common.h
@@ -77,6 +77,23 @@ void COMMON_clearbackground(int32_t numcols, int32_t numrows);
 #define EDUKE32_TMRTIC t[ti++]=getticks()
 #define EDUKE32_TMRPRN do { int ii=0; fprintf(stderr,"%s: ",tmrstr); for (ii=1; ii<ti; ii++) fprintf(stderr,"%d ", t[ii]-t[ii-1]); fprintf(stderr,"\n"); } while (0)
 
+// Get the multi-psky index corresponding to a base tile number of the sky (for
+// the game: the *static* value!), or -1 if it's not a multi-psky base tile.
+static inline int32_t MultiPsky_TileToIdx(int32_t tilenum)
+{
+    switch (tilenum)
+    {
+    case 80: // MOONSKY1__STATIC:
+        return 0;
+    case 84: // BIGORBIT1__STATIC:
+        return 1;
+    case 89: // LA__STATIC:
+        return 2;
+    default:
+        return -1;
+    }
+}
+
 #ifdef EXTERNC
 }
 #endif
diff --git a/polymer/eduke32/build/src/engine.c b/polymer/eduke32/build/src/engine.c
index 1a372e473..70081c285 100644
--- a/polymer/eduke32/build/src/engine.c
+++ b/polymer/eduke32/build/src/engine.c
@@ -4439,10 +4439,8 @@ static void parascan(int32_t dax1, int32_t dax2, int32_t sectnum, char dastat, i
     int32_t j, k, l, m, n, x, z, wallnum, nextsectnum, globalhorizbak;
     int16_t *topptr, *botptr;
 
-    int32_t dapyscale;
-    int16_t dapskybits;
-    static const int16_t zeropskyoff[MAXPSKYTILES] = { 0 };
-    const int16_t *dapskyoff;
+    int32_t dapyscale, dapskybits;
+    const int8_t *dapskyoff;
 
     int32_t logtilesizy, tsizy;
 
@@ -4499,32 +4497,19 @@ static void parascan(int32_t dax1, int32_t dax2, int32_t sectnum, char dastat, i
         globaltilesizy = tsizy;
         globalyscale = 65536 / tsizy;
         globalshiftval = 0;
-        globalzd = divscale32(((tsizy>>1)+parallaxyoffs), tsizy) + ((uint32_t)globalypanning<<24);
+        globalzd = divscale32(((tsizy>>1)+g_psky.yoffs), tsizy) + ((uint32_t)globalypanning<<24);
     }
     else
 #endif
     {
         globalshiftval = 32-globalshiftval;
         globalyscale = (8<<(globalshiftval-19));
-        globalzd = (((tsizy>>1)+parallaxyoffs)<<globalshiftval) + ((uint32_t)globalypanning<<24);
+        globalzd = (((tsizy>>1)+g_psky.yoffs)<<globalshiftval) + ((uint32_t)globalypanning<<24);
     }
 
     //if (globalorientation&256) globalyscale = -globalyscale, globalzd = -globalzd;
 
-    dapskyoff = zeropskyoff;
-    dapskybits = pskybits;
-    dapyscale = parallaxyscale;
-
-    for (j=0; j<pskynummultis; j++)
-    {
-        if (globalpicnum == pskymultilist[j])
-        {
-            dapskybits = pskymultibits[j];
-            dapskyoff = pskymultioff[j];
-            dapyscale = pskymultiyscale[j];
-            break;
-        }
-    }
+    dapskyoff = getpsky(&dapyscale, &dapskybits);
 
     if (dapyscale != 65536)
         globalhoriz = mulscale16(globalhoriz-(ydimen>>1),dapyscale) + (ydimen>>1);
@@ -8646,10 +8631,7 @@ int32_t initengine(void)
 
     xyaspect = -1;
 
-    pskyoff[0] = 0; pskybits = 0;
-    pskynummultis = 0;
-
-    parallaxtype = 2; parallaxyoffs = 0L; parallaxyscale = 65536;
+    parallaxtype = 2; g_psky.horizfrac = 65536;
     showinvisibility = 0;
 
     for (i=1; i<1024; i++)
diff --git a/polymer/eduke32/build/src/engine_priv.h b/polymer/eduke32/build/src/engine_priv.h
index ad2065506..8428cdbc4 100644
--- a/polymer/eduke32/build/src/engine_priv.h
+++ b/polymer/eduke32/build/src/engine_priv.h
@@ -212,4 +212,30 @@ static inline void bricolor(palette_t *wpptr, int32_t dacol)
     }
 }
 
+// Get properties of parallaxed sky to draw.
+// Returns: pointer to tile offset array. Sets-by-pointer the other two.
+static inline const int8_t *getpsky(int32_t *dapyscale, int32_t *dapskybits)
+{
+    int32_t j;
+    static const int8_t zeropskyoff[MAXPSKYTILES] = { 0 };
+
+    // First, try a multi-sky.
+    for (j=0; j<pskynummultis; j++)
+    {
+        if (globalpicnum == multipskytile[j])
+        {
+            // Have a match.
+            *dapskybits = multipsky[j].lognumtiles;
+            if (dapyscale)
+                *dapyscale = multipsky[j].horizfrac;
+            return multipsky[j].tileofs;
+        }
+    }
+
+    // Fall back to map-global sky.
+    *dapskybits = g_psky.lognumtiles;
+    if (dapyscale)
+        *dapyscale = g_psky.horizfrac;
+    return zeropskyoff;
+}
 #endif	/* ENGINE_PRIV_H */
diff --git a/polymer/eduke32/build/src/polymer.c b/polymer/eduke32/build/src/polymer.c
index ad1cbed80..5872c81c3 100644
--- a/polymer/eduke32/build/src/polymer.c
+++ b/polymer/eduke32/build/src/polymer.c
@@ -3874,16 +3874,15 @@ static void         polymer_initartsky(void)
 static void         polymer_drawartsky(int16_t tilenum, char palnum, int8_t shade)
 {
     pthtyp*         pth;
-    GLuint          glpics[5];
-    GLfloat         glcolors[5][3];
+    GLuint          glpics[PSKYOFF_MAX+1];
+    GLfloat         glcolors[PSKYOFF_MAX+1][3];
     int32_t         i, j;
     GLfloat         height = 2.45f / 2.0f;
-    int16_t         picnum;
 
     i = 0;
-    while (i < 5)
+    while (i <= PSKYOFF_MAX)
     {
-        picnum = tilenum + i;
+        int16_t picnum = tilenum + i;
         DO_TILE_ANIM(picnum, 0);
         if (!waloff[picnum])
             loadtile(picnum);
@@ -3915,13 +3914,14 @@ static void         polymer_drawartsky(int16_t tilenum, char palnum, int8_t shad
     }
 
     i = 0;
-    j = (1<<pskybits);
+    j = (1<<g_psky.lognumtiles);
     while (i < j)
     {
         GLint oldswrap;
+        const int8_t tileofs = g_psky.tileofs[i];
 
-        bglColor4f(glcolors[pskyoff[i]][0], glcolors[pskyoff[i]][1], glcolors[pskyoff[i]][2], 1.0f);
-        bglBindTexture(GL_TEXTURE_2D, glpics[pskyoff[i]]);
+        bglColor4f(glcolors[tileofs][0], glcolors[tileofs][1], glcolors[tileofs][2], 1.0f);
+        bglBindTexture(GL_TEXTURE_2D, glpics[tileofs]);
 
         bglGetTexParameteriv(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, &oldswrap);
         bglTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, glinfo.clamptoedge?GL_CLAMP_TO_EDGE:GL_CLAMP);
diff --git a/polymer/eduke32/build/src/polymost.c b/polymer/eduke32/build/src/polymost.c
index c4e633efe..9542ba9d5 100644
--- a/polymer/eduke32/build/src/polymost.c
+++ b/polymer/eduke32/build/src/polymost.c
@@ -2299,9 +2299,8 @@ static void polymost_drawalls(int32_t bunch)
     double oguo, ogux, oguy;
     int32_t i, x, y, z, cz, fz, wallnum, sectnum, nextsectnum;
 
-    int16_t dapskybits;
-    static const int16_t zeropskyoff[MAXPSKYTILES] = { 0 };
-    const int16_t *dapskyoff;
+    int32_t dapskybits;
+    const int8_t *dapskyoff;
 
     alpha = 0.f;
 
@@ -2369,20 +2368,7 @@ static void polymost_drawalls(int32_t bunch)
 
         DO_TILE_ANIM(globalpicnum, sectnum);
 
-        // multi-psky stuff
-        dapskyoff = zeropskyoff;
-        dapskybits = pskybits;
-
-        for (i=0; i<pskynummultis; i++)
-        {
-            if (globalpicnum == pskymultilist[i])
-            {
-                dapskybits = pskymultibits[i];
-                dapskyoff = pskymultioff[i];
-                break;
-            }
-        }
-        //
+        dapskyoff = getpsky(NULL, &dapskybits);
 
         global_cf_shade = sec->floorshade, global_cf_pal = sec->floorpal; global_cf_z = sec->floorz;  // REFACT
         global_cf_xpanning = sec->floorxpanning; global_cf_ypanning = sec->floorypanning, global_cf_heinum = sec->floorheinum;
@@ -2414,7 +2400,7 @@ static void polymost_drawalls(int32_t bunch)
                 dd[0] = (float)xdimen*.0000001; //Adjust sky depth based on screen size!
                 t = (double)((1<<(picsiz[globalpicnum]&15))<<dapskybits);
                 vv[1] = dd[0]*((double)xdimscale*(double)viewingrange)/(65536.0*65536.0);
-                vv[0] = dd[0]*((double)((tilesizy[globalpicnum]>>1)+parallaxyoffs)) - vv[1]*ghoriz;
+                vv[0] = dd[0]*((double)((tilesizy[globalpicnum]>>1)+g_psky.yoffs)) - vv[1]*ghoriz;
                 i = (1<<(picsiz[globalpicnum]>>4)); if (i != tilesizy[globalpicnum]) i += i;
 
                 //Hack to draw black rectangle below sky when looking down...
@@ -2649,20 +2635,7 @@ static void polymost_drawalls(int32_t bunch)
 
         DO_TILE_ANIM(globalpicnum, sectnum);
 
-        // multi-psky stuff
-        dapskyoff = zeropskyoff;
-        dapskybits = pskybits;
-
-        for (i=0; i<pskynummultis; i++)
-        {
-            if (globalpicnum == pskymultilist[i])
-            {
-                dapskybits = pskymultibits[i];
-                dapskyoff = pskymultioff[i];
-                break;
-            }
-        }
-        //
+        dapskyoff = getpsky(NULL, &dapskybits);
 
         global_cf_shade = sec->ceilingshade, global_cf_pal = sec->ceilingpal; global_cf_z = sec->ceilingz;  // REFACT
         global_cf_xpanning = sec->ceilingxpanning; global_cf_ypanning = sec->ceilingypanning, global_cf_heinum = sec->ceilingheinum;
@@ -2695,7 +2668,7 @@ static void polymost_drawalls(int32_t bunch)
                 dd[0] = (float)xdimen*.0000001; //Adjust sky depth based on screen size!
                 t = (double)((1<<(picsiz[globalpicnum]&15))<<dapskybits);
                 vv[1] = dd[0]*((double)xdimscale*(double)viewingrange)/(65536.0*65536.0);
-                vv[0] = dd[0]*((double)((tilesizy[globalpicnum]>>1)+parallaxyoffs)) - vv[1]*ghoriz;
+                vv[0] = dd[0]*((double)((tilesizy[globalpicnum]>>1)+g_psky.yoffs)) - vv[1]*ghoriz;
                 i = (1<<(picsiz[globalpicnum]>>4)); if (i != tilesizy[globalpicnum]) i += i;
 
                 //Hack to draw black rectangle below sky when looking down...
diff --git a/polymer/eduke32/source/astub.c b/polymer/eduke32/source/astub.c
index b7226238a..ed6ab2331 100644
--- a/polymer/eduke32/source/astub.c
+++ b/polymer/eduke32/source/astub.c
@@ -723,7 +723,7 @@ void ExtSetupMapFilename(const char *mapname)
 void ExtLoadMap(const char *mapname)
 {
     int32_t i;
-    int32_t sky=0;
+    int32_t mskyidx=0;
 
     getmessageleng = 0;
     getmessagetimeoff = 0;
@@ -732,39 +732,20 @@ void ExtLoadMap(const char *mapname)
 
     // old-fashioned multi-psky handling
 
-    Bmemset(pskyoff, 0, sizeof(pskyoff));
+    Bmemset(g_psky.tileofs, 0, sizeof(g_psky.tileofs));
 
     for (i=0; i<numsectors; i++)
     {
-        switch (sector[i].ceilingpicnum)
-        {
-        case MOONSKY1 :
-        case BIGORBIT1 : // orbit
-        case LA : // la city
-            sky=sector[i].ceilingpicnum;
+        mskyidx = MultiPsky_TileToIdx(sector[i].ceilingpicnum);
+        if (mskyidx >= 0)
             break;
-        }
     }
 
-    switch (sky)
-    {
-    case MOONSKY1 :
-        // keep in sync with G_MultiPskyInit
-        //                           -v-
-        Bmemcpy(pskyoff, pskymultioff[0], sizeof(pskymultioff[0]));
-        break;
+    if (mskyidx >= 0)
+        Bmemcpy(g_psky.tileofs, multipsky[mskyidx].tileofs, sizeof(g_psky.tileofs));
 
-    case BIGORBIT1 : // orbit
-        Bmemcpy(pskyoff, pskymultioff[1], sizeof(pskymultioff[0]));
-        break;
-
-    case LA : // la city
-        Bmemcpy(pskyoff, pskymultioff[2], sizeof(pskymultioff[0]));
-        break;
-    }
-
-    pskybits=3;
-    parallaxtype=0;
+    g_psky.lognumtiles = 3;
+    parallaxtype = 0;
 
     //////////
 #if M32_UNDO
@@ -10489,7 +10470,7 @@ int32_t ExtInit(void)
 
     ReadHelpFile("m32help.hlp");
 
-    G_MultiPskyInit();
+    G_MultiPskyInit(MOONSKY1, BIGORBIT1, LA);
 
 #ifdef LUNATIC
     if (Em_CreateState(&g_EmState) == 0)
diff --git a/polymer/eduke32/source/common.c b/polymer/eduke32/source/common.c
index e4cb92539..ad4815707 100644
--- a/polymer/eduke32/source/common.c
+++ b/polymer/eduke32/source/common.c
@@ -152,56 +152,72 @@ const char *G_ConFile(void)
 
 //////////
 
-void G_MultiPskyInit(void)
+// Set up new-style multi-psky handling.
+// NOTE: When adding more multi-pskies, take a look whether the engine-side
+// MAXPSKYMULTIS needs to be increased.
+void G_MultiPskyInit(int32_t MOONSKY1__DYN, int32_t BIGORBIT1__DYN, int32_t LA__DYN)
 {
     int32_t i;
 
-    // new-style multi-psky handling
-    pskymultilist[0] = MOONSKY1;
-    pskymultilist[1] = BIGORBIT1;
-    pskymultilist[2] = LA;
+    psky_t *moonsky = &multipsky[0];
+    psky_t *spacesky = &multipsky[1];
+    psky_t *citysky = &multipsky[2];
 
-    pskymultiyscale[0] = 32768;
-    pskymultiyscale[1] = 32768;
-    pskymultiyscale[2] = 16384+1024;
+    static int32_t inited;
+    if (inited)
+        return;
+    inited = 1;
 
-    for (i=0; i<3; ++i)
-    {
-        pskymultibits[i] = 3;
-        Bmemset(pskymultioff[i], 0, sizeof(pskymultioff[i]));
-    }
-
-    // KEEPINSYNC with Polymer MAX OFFSET = 4
-
-    // MOONSKY1
-    //        earth          mountain   mountain         sun
-    pskymultioff[0][6]=1;
-    pskymultioff[0][1]=2;
-    pskymultioff[0][4]=2;
-    pskymultioff[0][2]=3;
-
-    // BIGORBIT1   // orbit
-    //       earth1         2           3           moon/sun
-    pskymultioff[1][5]=1;
-    pskymultioff[1][6]=2;
-    pskymultioff[1][7]=3;
-    pskymultioff[1][2]=4;
-
-    // LA // la city
-    //       earth1         2           3           moon/sun
-    pskymultioff[2][0]=1;
-    pskymultioff[2][1]=2;
-    pskymultioff[2][2]=1;
-    pskymultioff[2][3]=3;
-    pskymultioff[2][4]=4;
-    pskymultioff[2][5]=0;
-    pskymultioff[2][6]=2;
-    pskymultioff[2][7]=3;
+    multipskytile[0] = MOONSKY1__DYN;
+    multipskytile[1] = BIGORBIT1__DYN;
+    multipskytile[2] = LA__DYN;
 
     pskynummultis = 3;
 
+    // When adding other multi-skies, take care that the tileofs[] values are
+    // <= PSKYOFF_MAX. (It can be increased up to MAXPSKYTILES, but should be
+    // set as tight as possible.)
+
+    // MOONSKY1
+    //        earth          mountain   mountain         sun
+    moonsky->lognumtiles = 3;
+    moonsky->horizfrac = 32768;
+    moonsky->tileofs[6] = 1;
+    moonsky->tileofs[1] = 2;
+    moonsky->tileofs[4] = 2;
+    moonsky->tileofs[2] = 3;
+
+    // BIGORBIT1   // orbit
+    //       earth1         2           3           moon/sun
+    spacesky->lognumtiles = 3;
+    spacesky->horizfrac = 32768;
+    spacesky->tileofs[5] = 1;
+    spacesky->tileofs[6] = 2;
+    spacesky->tileofs[7] = 3;
+    spacesky->tileofs[2] = 4;
+
+    // LA // la city
+    //       earth1         2           3           moon/sun
+    citysky->lognumtiles = 3;
+    citysky->horizfrac = 16384+1024;
+    citysky->tileofs[0] = 1;
+    citysky->tileofs[1] = 2;
+    citysky->tileofs[2] = 1;
+    citysky->tileofs[3] = 3;
+    citysky->tileofs[4] = 4;
+    citysky->tileofs[5] = 0;
+    citysky->tileofs[6] = 2;
+    citysky->tileofs[7] = 3;
+
+    for (i=0; i<pskynummultis; ++i)
+    {
+        int32_t j;
+        for (j=0; j<(1<<multipsky[i].lognumtiles); ++j)
+            Bassert(multipsky[i].tileofs[j] <= PSKYOFF_MAX);
+    }
+
     // default in game:
-    parallaxyscale = 32768;
+    g_psky.horizfrac = 32768;
 }
 
 //////////
diff --git a/polymer/eduke32/source/common_game.h b/polymer/eduke32/source/common_game.h
index ffa2bc46d..35a9ed4b5 100644
--- a/polymer/eduke32/source/common_game.h
+++ b/polymer/eduke32/source/common_game.h
@@ -58,7 +58,7 @@ extern void clearScriptNamePtr(void);
 
 //////////
 
-extern void G_MultiPskyInit(void);
+extern void G_MultiPskyInit(int32_t MOONSKY1__DYN, int32_t BIGORBIT1__DYN, int32_t LA__DYN);
 
 //////////
 
diff --git a/polymer/eduke32/source/duke3d.h b/polymer/eduke32/source/duke3d.h
index b3f219796..88752b12b 100644
--- a/polymer/eduke32/source/duke3d.h
+++ b/polymer/eduke32/source/duke3d.h
@@ -59,10 +59,10 @@ Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
 // increase by 3, because atomic GRP adds 1, and Shareware adds 2
 #ifdef LUNATIC
 // Lunatic
-# define BYTEVERSION_JF      279
+# define BYTEVERSION_JF      282
 #else
 // Non-Lua build
-# define BYTEVERSION_JF      279
+# define BYTEVERSION_JF      282
 #endif
 
 #define BYTEVERSION_13      27
diff --git a/polymer/eduke32/source/game.c b/polymer/eduke32/source/game.c
index 85485e1ae..901fb05ce 100644
--- a/polymer/eduke32/source/game.c
+++ b/polymer/eduke32/source/game.c
@@ -10719,6 +10719,7 @@ static void G_Startup(void)
     G_InitDynamicSounds();
 
     // These depend on having the dynamic tile and/or sound mappings set up:
+    G_MultiPskyInit(MOONSKY1, BIGORBIT1, LA);
     Gv_FinalizeWeaponDefaults();
     G_PostCreateGameState();
 
diff --git a/polymer/eduke32/source/gameexec.c b/polymer/eduke32/source/gameexec.c
index 8bc2df540..441121ef8 100644
--- a/polymer/eduke32/source/gameexec.c
+++ b/polymer/eduke32/source/gameexec.c
@@ -5537,8 +5537,8 @@ void G_SaveMapState(void)
         Bmemcpy(&save->clouds[0],&clouds[0],sizeof(clouds));
         Bmemcpy(&save->cloudx[0],&cloudx[0],sizeof(cloudx));
         Bmemcpy(&save->cloudy[0],&cloudy[0],sizeof(cloudy));
-        Bmemcpy(&save->pskyoff[0],&pskyoff[0],sizeof(pskyoff));
-        Bmemcpy(&save->pskybits,&pskybits,sizeof(pskybits));
+        Bmemcpy(&save->pskyoff[0],g_psky.tileofs,sizeof(g_psky.tileofs));
+        Bmemcpy(&save->pskybits,&g_psky.lognumtiles,sizeof(g_psky.lognumtiles));
         Bmemcpy(&save->animategoal[0],&animategoal[0],sizeof(animategoal));
         Bmemcpy(&save->animatevel[0],&animatevel[0],sizeof(animatevel));
         Bmemcpy(&save->g_animateCount,&g_animateCount,sizeof(g_animateCount));
@@ -5643,8 +5643,8 @@ void G_RestoreMapState(void)
         Bmemcpy(&clouds[0],&save->clouds[0],sizeof(clouds));
         Bmemcpy(&cloudx[0],&save->cloudx[0],sizeof(cloudx));
         Bmemcpy(&cloudy[0],&save->cloudy[0],sizeof(cloudy));
-        Bmemcpy(&pskyoff[0],&save->pskyoff[0],sizeof(pskyoff));
-        Bmemcpy(&pskybits,&save->pskybits,sizeof(pskybits));
+        Bmemcpy(g_psky.tileofs,&save->pskyoff[0],sizeof(g_psky.tileofs));
+        Bmemcpy(&g_psky.lognumtiles,&save->pskybits,sizeof(g_psky.lognumtiles));
         Bmemcpy(&animategoal[0],&save->animategoal[0],sizeof(animategoal));
         Bmemcpy(&animatevel[0],&save->animatevel[0],sizeof(animatevel));
         Bmemcpy(&g_animateCount,&save->g_animateCount,sizeof(g_animateCount));
diff --git a/polymer/eduke32/source/premap.c b/polymer/eduke32/source/premap.c
index 0b9791652..b877151f4 100644
--- a/polymer/eduke32/source/premap.c
+++ b/polymer/eduke32/source/premap.c
@@ -966,50 +966,31 @@ static void resetprestat(int32_t snum,int32_t g)
 
 static inline void G_SetupBackdrop(int16_t sky)
 {
-    static int32_t multiskiesinited=0;
+    // Get the static value of the base sky tile number.
+    const int32_t ssky = DYNAMICTILEMAP(sky);
 
-    if (!multiskiesinited)
+    Bmemset(g_psky.tileofs, 0, sizeof(g_psky.tileofs));
+
+    // XXX: why the condition?
+    if (g_psky.horizfrac != 65536)
+        g_psky.horizfrac = 32768;
+
+    if (ssky == CLOUDYOCEAN__STATIC)
     {
-        multiskiesinited = 1;
-        G_MultiPskyInit();
+        g_psky.horizfrac = 65536;
+    }
+    else
+    {
+        int32_t mskyidx = MultiPsky_TileToIdx(ssky);
+        if (mskyidx >= 0)
+        {
+            Bmemcpy(g_psky.tileofs, multipsky[mskyidx].tileofs, sizeof(g_psky.tileofs));
+            if (ssky == LA__STATIC)
+                g_psky.horizfrac = 16384+1024;
+        }
     }
 
-    Bmemset(pskyoff, 0, sizeof(pskyoff));
-
-    if (parallaxyscale != 65536)
-        parallaxyscale = 32768;
-
-    switch (DYNAMICTILEMAP(sky))
-    {
-    case CLOUDYOCEAN__STATIC:
-        parallaxyscale = 65536L;
-        break;
-    case MOONSKY1__STATIC :
-        pskyoff[6]=1;
-        pskyoff[1]=2;
-        pskyoff[4]=2;
-        pskyoff[2]=3;
-        break;
-    case BIGORBIT1__STATIC: // orbit
-        pskyoff[5]=1;
-        pskyoff[6]=2;
-        pskyoff[7]=3;
-        pskyoff[2]=4;
-        break;
-    case LA__STATIC:
-        parallaxyscale = 16384+1024;
-        pskyoff[0]=1;
-        pskyoff[1]=2;
-        pskyoff[2]=1;
-        pskyoff[3]=3;
-        pskyoff[4]=4;
-        pskyoff[5]=0;
-        pskyoff[6]=2;
-        pskyoff[7]=3;
-        break;
-    }
-
-    pskybits=3;
+    g_psky.lognumtiles = 3;
 }
 
 // tweak moving sectors with these SE lotags
@@ -1451,7 +1432,7 @@ void G_NewGame(int32_t vn, int32_t ln, int32_t sk)
     ud.player_skill = sk;
     ud.secretlevel = 0;
     ud.from_bonus = 0;
-    parallaxyscale = 0;
+    g_psky.horizfrac = 0;
 
     ud.last_level = -1;
     g_lastSaveSlot = -1;
diff --git a/polymer/eduke32/source/savegame.c b/polymer/eduke32/source/savegame.c
index 75dff9826..d3a0a75a9 100644
--- a/polymer/eduke32/source/savegame.c
+++ b/polymer/eduke32/source/savegame.c
@@ -139,6 +139,8 @@ void ReadSaveGameHeaders(void)
 
     savehead_t h;
 
+    EDUKE32_STATIC_ASSERT(sizeof(h.savename) == sizeof(ud.savegame[0]));
+
     Bstrcpy(fn, "dukesav0.esv");
 
     for (i=0; i<10; i++)
@@ -1026,9 +1028,7 @@ static const dataspec_t svgm_anmisc[] =
     { 0, &clouds[0], sizeof(clouds), 1 },
     { 0, &cloudx[0], sizeof(cloudx), 1 },
     { 0, &cloudy[0], sizeof(cloudy), 1 },
-    { DS_NOCHK, &parallaxyscale, sizeof(parallaxyscale), 1 },
-    { 0, &pskybits, sizeof(pskybits), 1 },
-    { 0, &pskyoff[0], sizeof(pskyoff[0]), MAXPSKYTILES },
+    { 0, &g_psky, sizeof(g_psky), 1 },  // DS_NOCHK?
     { 0, &g_earthquakeTime, sizeof(g_earthquakeTime), 1 },
 
     { DS_SAVEFN|DS_LOADFN|DS_NOCHK, (void *)sv_prequote, 0, 1 },
diff --git a/polymer/eduke32/source/savegame.h b/polymer/eduke32/source/savegame.h
index 8f614b80d..5a37a11b5 100644
--- a/polymer/eduke32/source/savegame.h
+++ b/polymer/eduke32/source/savegame.h
@@ -49,9 +49,11 @@ typedef struct
     uint8_t numplayers, volnum, levnum, skill;
     char boardfn[256];  // BMAX_PATH
     // 282 bytes
-} savehead_t;  // 310 bytes
+} savehead_t;
 #pragma pack(pop)
 
+EDUKE32_STATIC_ASSERT(sizeof(savehead_t) == 310);
+
 int32_t sv_updatestate(int32_t frominit);
 int32_t sv_readdiff(int32_t fil);
 uint32_t sv_writediff(FILE *fil);