diff --git a/gdk/gdkgl.c b/gdk/gdkgl.c
index d3b460b4b7..62eeada105 100644
--- a/gdk/gdkgl.c
+++ b/gdk/gdkgl.c
@@ -22,10 +22,6 @@
 
 #include "gdkinternals.h"
 
-#ifdef GDK_WINDOWING_WIN32
-# include "win32/gdkwin32.h"
-#endif
-
 #include <epoxy/gl.h>
 #include <math.h>
 #include <string.h>
@@ -633,13 +629,6 @@ gdk_cairo_draw_from_gl (cairo_t              *cr,
     {
       /* Software fallback */
       int major, minor, version;
-      gboolean es_read_bgra = FALSE;
-
-#ifdef GDK_WINDOWING_WIN32
-      /* on ANGLE GLES, we need to set the glReadPixel() format as GL_BGRA instead */
-      if (GDK_WIN32_IS_GL_CONTEXT(paint_context))
-        es_read_bgra = TRUE;
-#endif
 
       gdk_gl_context_get_version (paint_context, &major, &minor);
       version = major * 100 + minor;
@@ -681,8 +670,11 @@ gdk_cairo_draw_from_gl (cairo_t              *cr,
       if (!gdk_gl_context_get_use_es (paint_context))
         glReadPixels (x, y, width, height, GL_BGRA, GL_UNSIGNED_INT_8_8_8_8_REV,
                       cairo_image_surface_get_data (image));
+      else if (gdk_gl_context_has_texture_format_bgra (paint_context) && G_BYTE_ORDER == G_LITTLE_ENDIAN)
+        glReadPixels (x, y, width, height, GL_BGRA, GL_UNSIGNED_BYTE,
+                      cairo_image_surface_get_data (image));
       else
-        glReadPixels (x, y, width, height, es_read_bgra ? GL_BGRA : GL_RGBA, GL_UNSIGNED_BYTE,
+        glReadPixels (x, y, width, height, GL_RGBA, GL_UNSIGNED_BYTE,
                       cairo_image_surface_get_data (image));
 
       glPixelStorei (GL_PACK_ROW_LENGTH, 0);
diff --git a/gdk/gdkglcontext.c b/gdk/gdkglcontext.c
index 4c137a8d5d..80d126f2de 100644
--- a/gdk/gdkglcontext.c
+++ b/gdk/gdkglcontext.c
@@ -102,6 +102,7 @@ typedef struct {
   guint has_frame_terminator : 1;
   guint has_unpack_subimage : 1;
   guint has_sync : 1;
+  guint has_texture_format_bgra : 1;
   guint extensions_checked : 1;
   guint debug_enabled : 1;
   guint forward_compatible : 1;
@@ -450,6 +451,14 @@ gdk_gl_context_has_sync (GdkGLContext *context)
   return priv->has_sync;
 }
 
+gboolean
+gdk_gl_context_has_texture_format_bgra (GdkGLContext *context)
+{
+  GdkGLContextPrivate *priv = gdk_gl_context_get_instance_private (context);
+
+  return priv->has_texture_format_bgra;
+}
+
 /**
  * gdk_gl_context_set_debug_enabled:
  * @context: a #GdkGLContext
@@ -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_texture_format_bgra = epoxy_has_gl_extension ("GL_EXT_texture_format_BGRA8888");
     }
   else
     {
diff --git a/gdk/gdkglcontextprivate.h b/gdk/gdkglcontextprivate.h
index 94ecb34d30..731bf3e384 100644
--- a/gdk/gdkglcontextprivate.h
+++ b/gdk/gdkglcontextprivate.h
@@ -87,6 +87,7 @@ gboolean                gdk_gl_context_has_framebuffer_blit     (GdkGLContext
 gboolean                gdk_gl_context_has_frame_terminator     (GdkGLContext    *context);
 gboolean                gdk_gl_context_has_unpack_subimage      (GdkGLContext    *context);
 gboolean                gdk_gl_context_has_sync                 (GdkGLContext    *context);
+gboolean                gdk_gl_context_has_texture_format_bgra  (GdkGLContext    *context);
 void                    gdk_gl_context_end_frame                (GdkGLContext    *context,
                                                                  cairo_region_t  *painted,
                                                                  cairo_region_t  *damage);