diff --git a/gsk/gpu/gskglimage.c b/gsk/gpu/gskglimage.c
index d32008ba71..133c64a8ae 100644
--- a/gsk/gpu/gskglimage.c
+++ b/gsk/gpu/gskglimage.c
@@ -46,7 +46,7 @@ gsk_gl_image_finalize (GObject *object)
   if (self->texture_id && self->framebuffer_id)
     glDeleteFramebuffers (1, &self->framebuffer_id);
 
-  if (self->owns_texture)
+  if (gsk_gpu_image_get_flags (GSK_GPU_IMAGE (self)) & GSK_GPU_IMAGE_TOGGLE_REF)
     glDeleteTextures (1, &self->texture_id);
 
   G_OBJECT_CLASS (gsk_gl_image_parent_class)->finalize (object);
@@ -336,17 +336,17 @@ gsk_gl_image_get_gl_type (GskGLImage *self)
 }
 
 GLuint
-gsk_gl_image_steal_texture (GskGLImage *self)
+gsk_gl_image_get_texture_id (GskGLImage *self)
 {
-  g_assert (self->owns_texture);
-
-  if (self->framebuffer_id)
-    {
-      glDeleteFramebuffers (1, &self->framebuffer_id);
-      self->framebuffer_id = 0;
-    }
-
-  self->owns_texture = FALSE;
-
   return self->texture_id;
 }
+
+void
+gsk_gl_image_steal_texture_ownership (GskGLImage *self)
+{
+  g_assert (self->texture_id);
+  g_assert (self->owns_texture);
+
+  self->owns_texture = FALSE;
+}
+
diff --git a/gsk/gpu/gskglimageprivate.h b/gsk/gpu/gskglimageprivate.h
index 1d002f8e38..a4f83aa5a3 100644
--- a/gsk/gpu/gskglimageprivate.h
+++ b/gsk/gpu/gskglimageprivate.h
@@ -39,6 +39,7 @@ GLint                   gsk_gl_image_get_gl_internal_format             (GskGLIm
 GLenum                  gsk_gl_image_get_gl_format                      (GskGLImage             *self);
 GLenum                  gsk_gl_image_get_gl_type                        (GskGLImage             *self);
 
-GLuint                  gsk_gl_image_steal_texture                      (GskGLImage             *self);
+GLuint                  gsk_gl_image_get_texture_id                     (GskGLImage             *self);
+void                    gsk_gl_image_steal_texture_ownership            (GskGLImage             *self);
 
 G_END_DECLS
diff --git a/gsk/gpu/gskgpudownloadop.c b/gsk/gpu/gskgpudownloadop.c
index c3fa658919..967fc97a98 100644
--- a/gsk/gpu/gskgpudownloadop.c
+++ b/gsk/gpu/gskgpudownloadop.c
@@ -280,8 +280,7 @@ release_dmabuf_texture (gpointer data)
 {
   Texture *texture = data;
 
-  for (unsigned int i = 0; i < texture->dmabuf.n_planes; i++)
-    g_close (texture->dmabuf.planes[i].fd, NULL);
+  gdk_dmabuf_close_fds (&texture->dmabuf);
   g_free (texture);
 }
 #endif
@@ -300,7 +299,7 @@ gsk_gpu_download_op_gl_command (GskGpuOp          *op,
   /* Don't use the renderer context, the texture might survive the frame
    * and its surface */
   context = gdk_display_get_gl_context (gsk_gpu_device_get_display (gsk_gpu_frame_get_device (frame)));
-  texture_id = gsk_gl_image_steal_texture (GSK_GL_IMAGE (self->image));
+  texture_id = gsk_gl_image_get_texture_id (GSK_GL_IMAGE (self->image));
 
 #ifdef HAVE_DMABUF
   if (self->allow_dmabuf)
@@ -326,6 +325,8 @@ gsk_gpu_download_op_gl_command (GskGpuOp          *op,
 
           if (self->texture)
             return op->next;
+
+          gdk_dmabuf_close_fds (&texture->dmabuf);
         }
 
       g_free (texture);
@@ -351,6 +352,9 @@ gsk_gpu_download_op_gl_command (GskGpuOp          *op,
                                                 gsk_gl_texture_data_free,
                                                 data);
 
+  gsk_gpu_image_toggle_ref_texture (self->image, self->texture);
+  gsk_gl_image_steal_texture_ownership (GSK_GL_IMAGE (self->image));
+
   g_object_unref (builder);
 
   return op->next;