diff --git a/src/r_segs.cpp b/src/r_segs.cpp
index adbd5a3f9..9d97c0a29 100644
--- a/src/r_segs.cpp
+++ b/src/r_segs.cpp
@@ -1225,7 +1225,7 @@ void wallscan_drawcol1(int x, int y1, int y2, WallscanSampler &sampler, DWORD(*d
 	}
 	else
 	{
-		if (sampler.uv_max == 0) // power of two
+		if (sampler.uv_max == 0 || sampler.uv_step == 0) // power of two
 		{
 			int count = y2 - y1;
 
@@ -1300,7 +1300,7 @@ void wallscan_drawcol4(int x, int y1, int y2, WallscanSampler *sampler, void(*dr
 	}
 	else
 	{
-		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 2397fc48c..6276cb49e 100644
--- a/src/v_draw.cpp
+++ b/src/v_draw.cpp
@@ -1425,10 +1425,26 @@ void DCanvas::FillSimplePoly(FTexture *tex, FVector2 *points, int npoints,
 	else
 		R_SetSpanColormap(&identitycolormap, 0);
 	R_SetSpanSource(tex);
-	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;