diff --git a/cogl/cogl/cogl-blit.c b/cogl/cogl/cogl-blit.c
index 26a9b2993..07f0dde74 100644
--- a/cogl/cogl/cogl-blit.c
+++ b/cogl/cogl/cogl-blit.c
@@ -4,6 +4,7 @@
  * A Low Level GPU Graphics and Utilities API
  *
  * Copyright (C) 2011 Intel Corporation.
+ * Copyright (C) 2019 DisplayLink (UK) Ltd.
  *
  * Permission is hereby granted, free of charge, to any person
  * obtaining a copy of this software and associated documentation
@@ -152,10 +153,11 @@ _cogl_blit_framebuffer_begin (CoglBlitData *data)
   CoglFramebuffer *dst_fb, *src_fb;
   GError *ignore_error = NULL;
 
-  /* We can only blit between FBOs if both textures are the same
-     format and the blit framebuffer extension is supported */
-  if ((_cogl_texture_get_format (data->src_tex) & ~COGL_A_BIT) !=
-      (_cogl_texture_get_format (data->dst_tex) & ~COGL_A_BIT) ||
+  /* We can only blit between FBOs if both textures have the same
+     premult convention and the blit framebuffer extension is
+     supported. */
+  if ((_cogl_texture_get_format (data->src_tex) & COGL_PREMULT_BIT) !=
+      (_cogl_texture_get_format (data->dst_tex) & COGL_PREMULT_BIT) ||
       !_cogl_has_private_feature (ctx, COGL_PRIVATE_FEATURE_OFFSCREEN_BLIT))
     return FALSE;
 
diff --git a/cogl/cogl/cogl-framebuffer-private.h b/cogl/cogl/cogl-framebuffer-private.h
index 4e87a46b2..7b2560173 100644
--- a/cogl/cogl/cogl-framebuffer-private.h
+++ b/cogl/cogl/cogl-framebuffer-private.h
@@ -378,8 +378,12 @@ _cogl_push_framebuffers (CoglFramebuffer *draw_buffer,
  * This blits a region of the color buffer of the source buffer
  * to the destination buffer. This function should only be
  * called if the COGL_PRIVATE_FEATURE_OFFSCREEN_BLIT feature is
- * advertised. The two buffers must both be offscreen and have the
- * same format.
+ * advertised. The two buffers must both be offscreen.
+ *
+ * The two buffers must have the same value types (e.g. floating-point,
+ * unsigned int, signed int, or fixed-point), but color formats do not
+ * need to match. This limitation comes from OpenGL ES 3.0 definition
+ * of glBlitFramebuffer.
  *
  * Note that this function differs a lot from the glBlitFramebuffer
  * function provided by the GL_EXT_framebuffer_blit extension. Notably
diff --git a/cogl/cogl/cogl-framebuffer.c b/cogl/cogl/cogl-framebuffer.c
index de9bfb451..1c046476e 100644
--- a/cogl/cogl/cogl-framebuffer.c
+++ b/cogl/cogl/cogl-framebuffer.c
@@ -4,6 +4,7 @@
  * A Low Level GPU Graphics and Utilities API
  *
  * Copyright (C) 2007,2008,2009,2012 Intel Corporation.
+ * Copyright (C) 2019 DisplayLink (UK) Ltd.
  *
  * Permission is hereby granted, free of charge, to any person
  * obtaining a copy of this software and associated documentation
@@ -1360,8 +1361,9 @@ _cogl_blit_framebuffer (CoglFramebuffer *src,
      support this */
   g_return_if_fail (cogl_is_offscreen (src));
   g_return_if_fail (cogl_is_offscreen (dest));
-  /* The buffers must be the same format */
-  g_return_if_fail (src->internal_format == dest->internal_format);
+  /* The buffers must use the same premult convention */
+  g_return_if_fail ((src->internal_format & COGL_PREMULT_BIT) ==
+                    (dest->internal_format & COGL_PREMULT_BIT));
 
   /* Make sure the current framebuffers are bound. We explicitly avoid
      flushing the clip state so we can bind our own empty state */