diff --git a/gdk/gdkgl.c b/gdk/gdkgl.c
index d3b460b4b7..1c33f9941a 100644
--- a/gdk/gdkgl.c
+++ b/gdk/gdkgl.c
@@ -396,7 +396,14 @@ gdk_cairo_draw_from_gl (cairo_t              *cr,
   else if (source_type == GL_TEXTURE)
     {
       glBindTexture (GL_TEXTURE_2D, source);
-      glGetTexLevelParameteriv (GL_TEXTURE_2D, 0, GL_TEXTURE_ALPHA_SIZE,  &alpha_size);
+      if (gdk_gl_context_has_tex_param(paint_context))
+      {
+        glGetTexLevelParameteriv (GL_TEXTURE_2D, 0, GL_TEXTURE_ALPHA_SIZE,  &alpha_size);
+      }
+      else
+      {
+        alpha_size = 1;
+      }
     }
   else
     {
@@ -542,7 +549,8 @@ gdk_cairo_draw_from_gl (cairo_t              *cr,
 
       glBindTexture (GL_TEXTURE_2D, source);
 
-      if (gdk_gl_context_get_use_es (paint_context))
+      if (gdk_gl_context_get_use_es (paint_context) ||
+          !gdk_gl_context_has_tex_param (paint_context))
         {
           texture_width = width;
           texture_height = height;
diff --git a/gdk/gdkglcontext.c b/gdk/gdkglcontext.c
index 4c137a8d5d..35e1db7768 100644
--- a/gdk/gdkglcontext.c
+++ b/gdk/gdkglcontext.c
@@ -106,6 +106,7 @@ typedef struct {
   guint debug_enabled : 1;
   guint forward_compatible : 1;
   guint is_legacy : 1;
+  guint has_tex_param : 1;
 
   int use_es;
 
@@ -434,6 +435,14 @@ gdk_gl_context_has_frame_terminator (GdkGLContext *context)
   return priv->has_frame_terminator;
 }
 
+gboolean
+gdk_gl_context_has_tex_param (GdkGLContext *context)
+{
+  GdkGLContextPrivate *priv = gdk_gl_context_get_instance_private (context);
+
+  return priv->has_tex_param;
+}
+
 gboolean
 gdk_gl_context_has_unpack_subimage (GdkGLContext *context)
 {
@@ -819,6 +828,7 @@ gdk_gl_context_check_extensions (GdkGLContext *context)
 
       priv->has_unpack_subimage = epoxy_has_gl_extension ("GL_EXT_unpack_subimage");
       priv->has_sync = priv->gl_version >= 30;
+      priv->has_tex_param = priv->gl_version >= 31;
     }
   else
     {
@@ -828,6 +838,8 @@ gdk_gl_context_check_extensions (GdkGLContext *context)
       priv->has_gl_framebuffer_blit = priv->gl_version >= 30 || epoxy_has_gl_extension ("GL_EXT_framebuffer_blit");
       priv->has_frame_terminator = epoxy_has_gl_extension ("GL_GREMEDY_frame_terminator");
       priv->has_unpack_subimage = TRUE;
+      priv->has_tex_param = priv->gl_version >= 10 &&
+                            epoxy_is_desktop_gl();
       priv->has_sync = priv->gl_version >= 32 ||
                        epoxy_has_gl_extension ("GL_ARB_sync") ||
                        epoxy_has_gl_extension ("GL_APPLE_sync");
diff --git a/gdk/gdkglcontextprivate.h b/gdk/gdkglcontextprivate.h
index 94ecb34d30..3e538ac209 100644
--- a/gdk/gdkglcontextprivate.h
+++ b/gdk/gdkglcontextprivate.h
@@ -85,6 +85,7 @@ GdkGLContextPaintData * gdk_gl_context_get_paint_data           (GdkGLContext
 gboolean                gdk_gl_context_use_texture_rectangle    (GdkGLContext    *context);
 gboolean                gdk_gl_context_has_framebuffer_blit     (GdkGLContext    *context);
 gboolean                gdk_gl_context_has_frame_terminator     (GdkGLContext    *context);
+gboolean                gdk_gl_context_has_tex_param            (GdkGLContext    *context);
 gboolean                gdk_gl_context_has_unpack_subimage      (GdkGLContext    *context);
 gboolean                gdk_gl_context_has_sync                 (GdkGLContext    *context);
 void                    gdk_gl_context_end_frame                (GdkGLContext    *context,