diff --git a/core/rend/gles/gldraw.cpp b/core/rend/gles/gldraw.cpp
index 51c1a2ca8..e15d776d6 100644
--- a/core/rend/gles/gldraw.cpp
+++ b/core/rend/gles/gldraw.cpp
@@ -179,7 +179,7 @@ template <u32 Type, bool SortingEnabled>
 __forceinline
 	void SetGPState(const PolyParam* gp,u32 cflip=0)
 {
-	if (gp->pcw.Texture && gp->tsp.FilterMode > 1)
+	if (gp->pcw.Texture && gp->tsp.FilterMode > 1 && Type != ListType_Punch_Through)
 	{
 		ShaderUniforms.trilinear_alpha = 0.25 * (gp->tsp.MipMapD & 0x3);
 		if (gp->tsp.FilterMode == 2)
@@ -237,7 +237,8 @@ __forceinline
 		glcache.TexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
 	}
 
-	if (Type==ListType_Translucent)
+	// Apparently punch-through polys support blending, or at least some combinations
+	if (Type == ListType_Translucent || Type == ListType_Punch_Through)
 	{
 		glcache.Enable(GL_BLEND);
 		glcache.BlendFunc(SrcBlendGL[gp->tsp.SrcInstr],DstBlendGL[gp->tsp.DstInstr]);
diff --git a/core/rend/gles/gles.cpp b/core/rend/gles/gles.cpp
index fe54b88ba..e619c9b5f 100644
--- a/core/rend/gles/gles.cpp
+++ b/core/rend/gles/gles.cpp
@@ -271,10 +271,6 @@ void main() \n\
 			#if pp_IgnoreTexA==1 \n\
 				texcol.a=1.0;	 \n\
 			#endif\n\
-			\n\
-			#if cp_AlphaTest == 1 \n\
-				if (cp_AlphaTestValue>texcol.a) discard;\n\
-			#endif  \n\
 		#endif \n\
 		#if pp_ShadInstr==0 \n\
 		{ \n\
@@ -298,6 +294,11 @@ void main() \n\
 		} \n\
 		#endif\n\
 		\n\
+		#if cp_AlphaTest == 1 \n\
+			if (cp_AlphaTestValue > color.a) \n\
+				discard; \n\
+		#endif  \n\
+		\n\
 		#if pp_Offset==1 && pp_BumpMap == 0 \n\
 		{ \n\
 			color.rgb+=vtx_offs.rgb; \n\