diff --git a/gdk/gdkmemoryformat.c b/gdk/gdkmemoryformat.c
index 798f44c21d..eb6fafe297 100644
--- a/gdk/gdkmemoryformat.c
+++ b/gdk/gdkmemoryformat.c
@@ -331,6 +331,7 @@ struct _GdkMemoryFormatDescription
   gsize bytes_per_pixel;
   gsize alignment;
   GdkMemoryDepth depth;
+  const GdkMemoryFormat *fallbacks;
   struct {
     guint internal_format;
     guint format;
@@ -362,6 +363,9 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_BGRA,
@@ -380,6 +384,9 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_BGRA,
@@ -398,6 +405,9 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_RGBA,
@@ -415,6 +425,9 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_RGBA,
@@ -433,6 +446,9 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_BGRA,
@@ -451,6 +467,9 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_BGRA,
@@ -469,6 +488,9 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_RGBA,
@@ -486,6 +508,9 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_RGBA,
@@ -504,6 +529,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_BGRA,
@@ -522,6 +551,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_BGRA,
@@ -540,6 +573,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_RGBA,
@@ -557,6 +594,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA8,
         .format = GL_RGBA,
@@ -575,6 +616,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 3,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGB8,
         .format = GL_RGB,
@@ -592,6 +637,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 3,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGB8,
         .format = GL_BGR,
@@ -610,6 +659,13 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 6,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_U16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16_PREMULTIPLIED,
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGB16,
         .format = GL_RGB,
@@ -627,6 +683,12 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 8,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_U16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA16,
         .format = GL_RGBA,
@@ -644,6 +706,12 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 8,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_U16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R32G32B32A32_FLOAT,
+        GDK_MEMORY_R16G16B16A16_FLOAT,
+        GDK_MEMORY_R8G8B8A8,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA16,
         .format = GL_RGBA,
@@ -661,6 +729,12 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 6,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_FLOAT16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGB16F,
         .format = GL_RGB,
@@ -678,6 +752,11 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 8,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_FLOAT16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA16F,
         .format = GL_RGBA,
@@ -695,6 +774,11 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 8,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_FLOAT16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R32G32B32A32_FLOAT,
+        GDK_MEMORY_R8G8B8A8,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA16F,
         .format = GL_RGBA,
@@ -712,6 +796,12 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     12,
     .alignment = G_ALIGNOF (float),
     .depth = GDK_MEMORY_FLOAT32,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGB32F,
         .format = GL_RGB,
@@ -729,6 +819,11 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     16,
     .alignment = G_ALIGNOF (float),
     .depth = GDK_MEMORY_FLOAT32,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA32F,
         .format = GL_RGBA,
@@ -746,6 +841,11 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     16,
     .alignment = G_ALIGNOF (float),
     .depth = GDK_MEMORY_FLOAT32,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16_FLOAT,
+        GDK_MEMORY_R8G8B8A8,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RGBA32F,
         .format = GL_RGBA,
@@ -763,6 +863,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 2,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RG8,
         .format = GL_RG,
@@ -780,6 +884,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 2,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RG8,
         .format = GL_RG,
@@ -797,6 +905,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 1,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_R8,
         .format = GL_RED,
@@ -814,6 +926,13 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_U16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16_PREMULTIPLIED,
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RG16,
         .format = GL_RG,
@@ -831,6 +950,13 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_U16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16,
+        GDK_MEMORY_R32G32B32A32_FLOAT,
+        GDK_MEMORY_R16G16B16A16_FLOAT,
+        GDK_MEMORY_R8G8B8A8,
+        -1,
+    },
     .gl = {
         .internal_format = GL_RG16,
         .format = GL_RG,
@@ -848,6 +974,13 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 2,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_U16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16_PREMULTIPLIED,
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_R16,
         .format = GL_RED,
@@ -865,6 +998,10 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 1,
     .alignment = G_ALIGNOF (guchar),
     .depth = GDK_MEMORY_U8,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_R8,
         .format = GL_RED,
@@ -882,6 +1019,13 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 2,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_U16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16_PREMULTIPLIED,
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_R16,
         .format = GL_RED,
@@ -899,6 +1043,12 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 2,
     .alignment = G_ALIGNOF (guint16),
     .depth = GDK_MEMORY_FLOAT16,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_R16F,
         .format = GL_RED,
@@ -916,6 +1066,12 @@ static const GdkMemoryFormatDescription memory_formats[] = {
     .bytes_per_pixel = 4,
     .alignment = G_ALIGNOF (float),
     .depth = GDK_MEMORY_FLOAT32,
+    .fallbacks = (GdkMemoryFormat[]) {
+        GDK_MEMORY_R32G32B32A32_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R16G16B16A16_FLOAT_PREMULTIPLIED,
+        GDK_MEMORY_R8G8B8A8_PREMULTIPLIED,
+        -1,
+    },
     .gl = {
         .internal_format = GL_R32F,
         .format = GL_RED,
@@ -961,6 +1117,34 @@ gdk_memory_format_alignment (GdkMemoryFormat format)
   return memory_formats[format].alignment;
 }
 
+/*
+ * gdk_memory_format_get_fallbacks:
+ * @format: a format
+ *
+ * Gets a list of fallback formats to use for @format.
+ *
+ * These formats are RGBA formats that ideally have a
+ * higher depth than the given format. They will always
+ * include a guaranteed supported format though, even
+ * if it is of lower quality.
+ *
+ * Fallbacks will use the same alpha format, ie a premultiplied
+ * format will never fall back to a straight alpha format and
+ * vice versa.
+ * Either may fall back to an opaque format.
+ * Opaque formats will fall back to premultiplied formats only.
+ *
+ * Use gdk_memory_format_get_premultiplied_formats() to transition
+ * between premultiplied and straight alpha if you need to.
+ *
+ * Returns: A list of fallbacks, terminated with -1
+ **/
+const GdkMemoryFormat *
+gdk_memory_format_get_fallbacks (GdkMemoryFormat format)
+{
+  return memory_formats[format].fallbacks;
+}
+
 /*<private>
  * gdk_memory_format_get_depth:
  * @format: a memory format
diff --git a/gdk/gdkmemoryformatprivate.h b/gdk/gdkmemoryformatprivate.h
index 14ef556b87..94764a3ee5 100644
--- a/gdk/gdkmemoryformatprivate.h
+++ b/gdk/gdkmemoryformatprivate.h
@@ -44,6 +44,7 @@ GdkMemoryAlpha          gdk_memory_format_alpha             (GdkMemoryFormat
 gsize                   gdk_memory_format_bytes_per_pixel   (GdkMemoryFormat             format) G_GNUC_CONST;
 GdkMemoryFormat         gdk_memory_format_get_premultiplied (GdkMemoryFormat             format) G_GNUC_CONST;
 GdkMemoryFormat         gdk_memory_format_get_straight      (GdkMemoryFormat             format) G_GNUC_CONST;
+const GdkMemoryFormat * gdk_memory_format_get_fallbacks     (GdkMemoryFormat             format) G_GNUC_CONST;
 GdkMemoryDepth          gdk_memory_format_get_depth         (GdkMemoryFormat             format) G_GNUC_CONST;
 GdkMemoryDepth          gdk_memory_depth_merge              (GdkMemoryDepth              depth1,
                                                              GdkMemoryDepth              depth2) G_GNUC_CONST;
diff --git a/gsk/gl/gskglcommandqueue.c b/gsk/gl/gskglcommandqueue.c
index 6e9c96494b..d560919f31 100644
--- a/gsk/gl/gskglcommandqueue.c
+++ b/gsk/gl/gskglcommandqueue.c
@@ -1483,8 +1483,9 @@ memory_format_gl_format (GdkMemoryFormat  data_format,
                          GLint            gl_swizzle[4])
 {
   GdkGLMemoryFlags flags;
-  GdkMemoryDepth depth;
   GdkMemoryFormat alt_format;
+  const GdkMemoryFormat *fallbacks;
+  gsize i;
 
   /* No support for straight formats yet */
   if (gdk_memory_format_alpha (data_format) == GDK_MEMORY_ALPHA_STRAIGHT)
@@ -1516,45 +1517,25 @@ memory_format_gl_format (GdkMemoryFormat  data_format,
         return data_format;
     }
 
-  /* Next, try the generic format for the given bit depth */
-  depth = gdk_memory_format_get_depth (data_format);
-  data_format = gdk_memory_depth_get_format (depth);
-  flags = gdk_gl_context_get_format_flags (context, data_format);
-  if (((flags & (GDK_GL_FORMAT_USABLE | GDK_GL_FORMAT_FILTERABLE)) == (GDK_GL_FORMAT_USABLE | GDK_GL_FORMAT_FILTERABLE)))
+  /* Next, try the fallbacks */
+  fallbacks = gdk_memory_format_get_fallbacks (data_format);
+  for (i = 0; fallbacks[i] != -1; i++)
     {
-      gdk_memory_format_gl_format (data_format,
-                                   gl_internalformat,
-                                   gl_format,
-                                   gl_type,
-                                   gl_swizzle);
-      return data_format;
-    }
-
-  /* If the format is high depth, also try float32 */
-  if (depth != GDK_MEMORY_U8)
-    {
-      flags = gdk_gl_context_get_format_flags (context, data_format);
+      flags = gdk_gl_context_get_format_flags (context, fallbacks[i]);
       if (((flags & (GDK_GL_FORMAT_USABLE | GDK_GL_FORMAT_FILTERABLE)) == (GDK_GL_FORMAT_USABLE | GDK_GL_FORMAT_FILTERABLE)))
         {
-          gdk_memory_format_gl_format (data_format,
+          gdk_memory_format_gl_format (fallbacks[i],
                                        gl_internalformat,
                                        gl_format,
                                        gl_type,
                                        gl_swizzle);
-          return data_format;
+          return fallbacks[i];
         }
     }
 
-  /* If all else fails, pick the one format that's always supported */
-  data_format = GDK_MEMORY_R8G8B8A8_PREMULTIPLIED;
-  g_assert ((gdk_gl_context_get_format_flags (context, data_format) & (GDK_GL_FORMAT_USABLE | GDK_GL_FORMAT_FILTERABLE)) == (GDK_GL_FORMAT_USABLE | GDK_GL_FORMAT_FILTERABLE));
-  gdk_memory_format_gl_format (data_format,
-                               gl_internalformat,
-                               gl_format,
-                               gl_type,
-                               gl_swizzle);
+  g_assert_not_reached ();
 
-  return data_format;
+  return GDK_MEMORY_R8G8B8A8_PREMULTIPLIED;
 }
 
 static void