diff --git a/plug-ins/file-webp/file-webp-load.c b/plug-ins/file-webp/file-webp-load.c
index 81ab934df4ccd13c9af41fd649834a6e03c8de6b..ac6832eb95c8af39467a8ef60e9b0cdbbc6ee44e 100644
--- a/plug-ins/file-webp/file-webp-load.c
+++ b/plug-ins/file-webp/file-webp-load.c
@@ -144,7 +144,10 @@ load_image (const gchar *filename,
 
       /* Check to ensure the image data was loaded correctly */
       if (! outdata)
-        return -1;
+        {
+          WebPMuxDelete (mux);
+          return -1;
+        }
 
       create_layer (image_ID, outdata, 0, _("Background"),
                     width, height);
@@ -173,6 +176,7 @@ load_image (const gchar *filename,
               WebPDemuxDelete (demux);
             }
 
+          WebPMuxDelete (mux);
           return -1;
         }
 
@@ -277,6 +281,8 @@ load_image (const gchar *filename,
       g_object_unref (file);
     }
 
+  WebPMuxDelete (mux);
+
   gimp_image_set_filename (image_ID, filename);
 
   return image_ID;
diff --git a/plug-ins/file-webp/file-webp-save.c b/plug-ins/file-webp/file-webp-save.c
index 9968e6f20c420b7f78e7f584851b5fecfc088c73..3aa3818d00943cf138f36402b7a1373d0092df10 100644
--- a/plug-ins/file-webp/file-webp-save.c
+++ b/plug-ins/file-webp/file-webp-save.c
@@ -316,6 +316,8 @@ save_layer (const gchar    *filename,
                   rewind (outfile);
                   webp_anim_file_writer (outfile, wp_data.bytes, wp_data.size);
                 }
+
+              WebPMuxDelete (mux);
             }
           else
             {