diff --git a/src/am_map.cpp b/src/am_map.cpp
index 9292e81d9..d74927b68 100644
--- a/src/am_map.cpp
+++ b/src/am_map.cpp
@@ -2046,7 +2046,8 @@ void AM_drawSubsectors()
 				scale / scaley,
 				rotation,
 				colormap,
-				floorlight
+				floorlight,
+				f_y + f_h
 				);
 		}
 	}
diff --git a/src/r_segs.cpp b/src/r_segs.cpp
index ae33332de..369722242 100644
--- a/src/r_segs.cpp
+++ b/src/r_segs.cpp
@@ -1114,7 +1114,7 @@ WallscanSampler::WallscanSampler(int y1, float swal, double yrepeat, fixed_t xof
 // Draw a column with support for non-power-of-two ranges
 void wallscan_drawcol1(int x, int y1, int y2, WallscanSampler &sampler, DWORD(*draw1column)())
 {
-	if (sampler.uv_max == 0) // power of two
+	if (sampler.uv_max == 0 || sampler.uv_step == 0) // power of two
 	{
 		int count = y2 - y1;
 
@@ -1162,7 +1162,7 @@ void wallscan_drawcol1(int x, int y1, int y2, WallscanSampler &sampler, DWORD(*d
 // Draw four columns with support for non-power-of-two ranges
 void wallscan_drawcol4(int x, int y1, int y2, WallscanSampler *sampler, void(*draw4columns)())
 {
-	if (sampler[0].uv_max == 0) // power of two, no wrap handling needed
+	if (sampler[0].uv_max == 0 || sampler[0].uv_step == 0) // power of two, no wrap handling needed
 	{
 		int count = y2 - y1;
 		for (int i = 0; i < 4; i++)
diff --git a/src/v_draw.cpp b/src/v_draw.cpp
index bef732894..8483b9844 100644
--- a/src/v_draw.cpp
+++ b/src/v_draw.cpp
@@ -1282,7 +1282,7 @@ void DCanvas::FinishSimplePolys()
 
 void DCanvas::FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 	double originx, double originy, double scalex, double scaley, DAngle rotation,
-	FDynamicColormap *colormap, int lightlevel)
+	FDynamicColormap *colormap, int lightlevel, int bottomclip)
 {
 #ifndef NO_SWRENDER
 	// Use an equation similar to player sprites to determine shade
@@ -1300,6 +1300,11 @@ void DCanvas::FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 		return;
 	}
 
+	if (bottomclip <= 0)
+	{
+		bottomclip = Height;
+	}
+
 	// Find the extents of the polygon, in particular the highest and lowest points.
 	for (botpt = toppt = 0, boty = topy = points[0].Y, leftx = rightx = points[0].X, i = 1; i <= npoints; ++i)
 	{
@@ -1322,7 +1327,7 @@ void DCanvas::FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 			rightx = points[i].X;
 		}
 	}
-	if (topy >= Height ||		// off the bottom of the screen
+	if (topy >= bottomclip ||	// off the bottom of the screen
 		boty <= 0 ||			// off the top of the screen
 		leftx >= Width ||		// off the right of the screen
 		rightx <= 0)			// off the left of the screen
@@ -1348,10 +1353,26 @@ void DCanvas::FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 	R_SetupSpanBits(tex);
 	R_SetSpanColormap(colormap != NULL ? &colormap->Maps[clamp(shade >> FRACBITS, 0, NUMCOLORMAPS-1) * 256] : identitymap);
 	R_SetSpanSource(tex->GetPixels());
-	scalex = double(1u << (32 - ds_xbits)) / scalex;
-	scaley = double(1u << (32 - ds_ybits)) / scaley;
-	ds_xstep = xs_RoundToInt(cosrot * scalex);
-	ds_ystep = xs_RoundToInt(sinrot * scaley);
+	if (ds_xbits != 0)
+	{
+		scalex = double(1u << (32 - ds_xbits)) / scalex;
+		ds_xstep = xs_RoundToInt(cosrot * scalex);
+	}
+	else
+	{ // Texture is one pixel wide.
+		scalex = 0;
+		ds_xstep = 0;
+	}
+	if (ds_ybits != 0)
+	{
+		scaley = double(1u << (32 - ds_ybits)) / scaley;
+		ds_ystep = xs_RoundToInt(sinrot * scaley);
+	}
+	else
+	{ // Texture is one pixel tall.
+		scaley = 0;
+		ds_ystep = 0;
+	}
 
 	// Travel down the right edge and create an outline of that edge.
 	pt1 = toppt;
@@ -1361,13 +1382,13 @@ void DCanvas::FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 	{
 		x = FLOAT2FIXED(points[pt1].X + 0.5f);
 		y2 = xs_RoundToInt(points[pt2].Y + 0.5f);
-		if (y1 >= y2 || (y1 < 0 && y2 < 0) || (y1 >= Height && y2 >= Height))
+		if (y1 >= y2 || (y1 < 0 && y2 < 0) || (y1 >= bottomclip && y2 >= bottomclip))
 		{
 		}
 		else
 		{
 			fixed_t xinc = FLOAT2FIXED((points[pt2].X - points[pt1].X) / (points[pt2].Y - points[pt1].Y));
-			int y3 = MIN(y2, Height);
+			int y3 = MIN(y2, bottomclip);
 			if (y1 < 0)
 			{
 				x += xinc * -y1;
@@ -1392,13 +1413,13 @@ void DCanvas::FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 	{
 		x = FLOAT2FIXED(points[pt1].X + 0.5f);
 		y2 = xs_RoundToInt(points[pt2].Y + 0.5f);
-		if (y1 >= y2 || (y1 < 0 && y2 < 0) || (y1 >= Height && y2 >= Height))
+		if (y1 >= y2 || (y1 < 0 && y2 < 0) || (y1 >= bottomclip && y2 >= bottomclip))
 		{
 		}
 		else
 		{
 			fixed_t xinc = FLOAT2FIXED((points[pt2].X - points[pt1].X) / (points[pt2].Y - points[pt1].Y));
-			int y3 = MIN(y2, Height);
+			int y3 = MIN(y2, bottomclip);
 			if (y1 < 0)
 			{
 				x += xinc * -y1;
diff --git a/src/v_video.h b/src/v_video.h
index d19a3b06e..890ab6d63 100644
--- a/src/v_video.h
+++ b/src/v_video.h
@@ -224,7 +224,7 @@ public:
 	// Fill a simple polygon with a texture
 	virtual void FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 		double originx, double originy, double scalex, double scaley, DAngle rotation,
-		struct FDynamicColormap *colormap, int lightlevel);
+		struct FDynamicColormap *colormap, int lightlevel, int bottomclip);
 
 	// Set an area to a specified color
 	virtual void Clear (int left, int top, int right, int bottom, int palcolor, uint32 color);
diff --git a/src/win32/fb_d3d9.cpp b/src/win32/fb_d3d9.cpp
index 8bb680dbd..10ab11c72 100644
--- a/src/win32/fb_d3d9.cpp
+++ b/src/win32/fb_d3d9.cpp
@@ -3084,11 +3084,16 @@ void D3DFB::FlatFill(int left, int top, int right, int bottom, FTexture *src, bo
 //
 // Here, "simple" means that a simple triangle fan can draw it.
 //
+// Bottomclip is ignored by this implementation, since the hardware renderer
+// will unconditionally draw the status bar border every frame on top of the
+// polygons, so there's no need to waste time setting up a special scissor
+// rectangle here and needlessly forcing separate batches.
+//
 //==========================================================================
 
 void D3DFB::FillSimplePoly(FTexture *texture, FVector2 *points, int npoints,
 	double originx, double originy, double scalex, double scaley,
-	DAngle rotation, FDynamicColormap *colormap, int lightlevel)
+	DAngle rotation, FDynamicColormap *colormap, int lightlevel, int bottomclip)
 {
 	// Use an equation similar to player sprites to determine shade
 	double fadelevel = clamp((LIGHT2SHADE(lightlevel)/65536. - 12) / NUMCOLORMAPS, 0.0, 1.0);
@@ -3109,7 +3114,7 @@ void D3DFB::FillSimplePoly(FTexture *texture, FVector2 *points, int npoints,
 	}
 	if (In2D < 2)
 	{
-		Super::FillSimplePoly(texture, points, npoints, originx, originy, scalex, scaley, rotation, colormap, lightlevel);
+		Super::FillSimplePoly(texture, points, npoints, originx, originy, scalex, scaley, rotation, colormap, lightlevel, bottomclip);
 		return;
 	}
 	if (!InScene)
diff --git a/src/win32/win32iface.h b/src/win32/win32iface.h
index 9b2754eae..b5262089b 100644
--- a/src/win32/win32iface.h
+++ b/src/win32/win32iface.h
@@ -265,7 +265,7 @@ public:
 	void DrawPixel(int x, int y, int palcolor, uint32 rgbcolor);
 	void FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 		double originx, double originy, double scalex, double scaley,
-		DAngle rotation, FDynamicColormap *colormap, int lightlevel);
+		DAngle rotation, FDynamicColormap *colormap, int lightlevel, int bottomclip) override;
 	bool WipeStartScreen(int type);
 	void WipeEndScreen();
 	bool WipeDo(int ticks);