diff --git a/src/asm_ia32/tmap2.asm b/src/asm_ia32/tmap2.asm
index 9a7aa5534..ab1695d3c 100644
--- a/src/asm_ia32/tmap2.asm
+++ b/src/asm_ia32/tmap2.asm
@@ -198,7 +198,10 @@ SetTiltedSpanSize:
 	mov	[y8+2],cl
 	mov	[y9+2],cl
 	mov	[y10+2],cl
+	cmp	eax,0		; if x bits is 0, mask must be 0 too.
+	jz	.notted
 	not	eax
+.notted:
 	pop	ecx
 	
 	mov	[m1+2],eax
diff --git a/src/r_plane.cpp b/src/r_plane.cpp
index f238c47d0..21cea7bcf 100644
--- a/src/r_plane.cpp
+++ b/src/r_plane.cpp
@@ -224,10 +224,26 @@ void R_MapPlane (int y, int x1)
 
 	distance = planeheight * yslope[y];
 
-	ds_xstep = xs_ToFixed(32-ds_xbits, distance * xstepscale);
-	ds_ystep = xs_ToFixed(32-ds_ybits, distance * ystepscale);
-	ds_xfrac = xs_ToFixed(32-ds_xbits, distance * basexfrac) + pviewx;
-	ds_yfrac = xs_ToFixed(32-ds_ybits, distance * baseyfrac) + pviewy;
+	if (ds_xbits != 0)
+	{
+		ds_xstep = xs_ToFixed(32 - ds_xbits, distance * xstepscale);
+		ds_xfrac = xs_ToFixed(32 - ds_xbits, distance * basexfrac) + pviewx;
+	}
+	else
+	{
+		ds_xstep = 0;
+		ds_xfrac = 0;
+	}
+	if (ds_ybits != 0)
+	{
+		ds_ystep = xs_ToFixed(32 - ds_ybits, distance * ystepscale);
+		ds_yfrac = xs_ToFixed(32 - ds_ybits, distance * baseyfrac) + pviewy;
+	}
+	else
+	{
+		ds_ystep = 0;
+		ds_yfrac = 0;
+	}
 
 	if (plane_shade)
 	{
@@ -368,18 +384,18 @@ void R_MapTiltedPlane_C (int y, int x1)
 	DWORD u, v;
 	int i;
 
-	iz = plane_sz[2] + plane_sz[1]*(centery-y) + plane_sz[0]*(x1-centerx);
+	iz = plane_sz[2] + plane_sz[1] * (centery - y) + plane_sz[0] * (x1 - centerx);
 
 	// Lighting is simple. It's just linear interpolation from start to end
 	if (plane_shade)
 	{
-		uz = (iz + plane_sz[0]*width) * planelightfloat;
+		uz = (iz + plane_sz[0] * width) * planelightfloat;
 		vz = iz * planelightfloat;
-		R_CalcTiltedLighting (vz, uz, width);
+		R_CalcTiltedLighting(vz, uz, width);
 	}
 
-	uz = plane_su[2] + plane_su[1]*(centery-y) + plane_su[0]*(x1-centerx);
-	vz = plane_sv[2] + plane_sv[1]*(centery-y) + plane_sv[0]*(x1-centerx);
+	uz = plane_su[2] + plane_su[1] * (centery - y) + plane_su[0] * (x1 - centerx);
+	vz = plane_sv[2] + plane_sv[1] * (centery - y) + plane_sv[0] * (x1 - centerx);
 
 	fb = ylookup[y] + x1 + dc_destorg;
 
@@ -2116,6 +2132,15 @@ void R_DrawTiltedPlane (visplane_t *pl, double _xscale, double _yscale, fixed_t
 		}
 	}
 
+	// Hack in support for 1 x Z and Z x 1 texture sizes
+	if (ds_ybits == 0)
+	{
+		plane_sv[2] = plane_sv[1] = plane_sv[0] = 0;
+	}
+	if (ds_xbits == 0)
+	{
+		plane_su[2] = plane_su[1] = plane_su[0] = 0;
+	}
 #if defined(X86_ASM)
 	if (!r_swtruecolor)
 	{
diff --git a/src/r_segs.cpp b/src/r_segs.cpp
index 8c00faa7f..108463e38 100644
--- a/src/r_segs.cpp
+++ b/src/r_segs.cpp
@@ -1093,21 +1093,31 @@ WallscanSampler::WallscanSampler(int y1, float swal, double yrepeat, fixed_t xof
 	if (!r_swtruecolor)
 	{
 		height = texture->GetHeight();
+
 		int uv_fracbits = 32 - texture->HeightBits;
-		uv_max = height << uv_fracbits;
+		if (uv_fracbits != 32)
+		{
+			uv_max = height << uv_fracbits;
 
-		// Find start uv in [0-base_height[ range.
-		// Not using xs_ToFixed because it rounds the result and we need something that always rounds down to stay within the range.
-		double uv_stepd = swal * yrepeat;
-		double v = (dc_texturemid + uv_stepd * (y1 - CenterY + 0.5)) / height;
-		v = v - floor(v);
-		v *= height;
-		v *= (1 << uv_fracbits);
+			// Find start uv in [0-base_height[ range.
+			// Not using xs_ToFixed because it rounds the result and we need something that always rounds down to stay within the range.
+			double uv_stepd = swal * yrepeat;
+			double v = (dc_texturemid + uv_stepd * (y1 - CenterY + 0.5)) / height;
+			v = v - floor(v);
+			v *= height;
+			v *= (1 << uv_fracbits);
 
-		uv_pos = (uint32_t)v;
-		uv_step = xs_ToFixed(uv_fracbits, uv_stepd);
-		if (uv_step == 0) // To prevent divide by zero elsewhere
-			uv_step = 1;
+			uv_pos = (uint32_t)v;
+			uv_step = xs_ToFixed(uv_fracbits, uv_stepd);
+			if (uv_step == 0) // To prevent divide by zero elsewhere
+				uv_step = 1;
+		}
+		else
+		{ // Hack for one pixel tall textures
+			uv_pos = 0;
+			uv_step = 0;
+			uv_max = 1;
+		}
 
 		source = getcol(texture, xoffset >> FRACBITS);
 		source2 = nullptr;
@@ -1368,11 +1378,19 @@ void wallscan_any(
 		return;
 
 	fixed_t xoffset = rw_offset;
+
 	rw_pic->GetHeight(); // To ensure that rw_pic->HeightBits has been set
+	int fracbits = 32 - rw_pic->HeightBits;
+	if (fracbits == 32)
+	{ // Hack for one pixel tall textures
+		fracbits = 0;
+		yrepeat = 0;
+		dc_texturemid = 0;
+	}
 
 	DWORD(*draw1column)();
 	void(*draw4columns)();
-	setupwallscan(r_swtruecolor ? FRACBITS : 32 - rw_pic->HeightBits, draw1column, draw4columns);
+	setupwallscan(r_swtruecolor ? FRACBITS : fracbits, draw1column, draw4columns);
 
 	bool fixed = (fixedcolormap != NULL || fixedlightlev >= 0);
 	if (fixed)
diff --git a/src/textures/texture.cpp b/src/textures/texture.cpp
index 04e62bed9..5774a0048 100644
--- a/src/textures/texture.cpp
+++ b/src/textures/texture.cpp
@@ -241,8 +241,9 @@ void FTexture::CalcBitSize ()
 	}
 	WidthMask = (1 << WidthBits) - 1;
 
-	// The minimum height is 2, because we cannot shift right 32 bits.
-	for (i = 1; (1 << i) < Height; ++i)
+	// <hr>The minimum height is 2, because we cannot shift right 32 bits.</hr>
+	// Scratch that. Somebody actually made a 1x1 texture, so now we have to handle it.
+	for (i = 0; (1 << i) < Height; ++i)
 	{ }
 
 	HeightBits = i;