diff --git a/debian/libwiretap0.symbols b/debian/libwiretap0.symbols
index 400458cfb2..0f7e397ab0 100644
--- a/debian/libwiretap0.symbols
+++ b/debian/libwiretap0.symbols
@@ -97,6 +97,7 @@ libwiretap.so.0 libwiretap0 #MINVER#
  wtap_free_idb_info@Base 1.99.9
  wtap_fstat@Base 1.9.1
  wtap_get_all_capture_file_extensions_list@Base 2.3.0
+ wtap_get_all_file_extensions_list@Base 2.6.2
  wtap_get_buf_ptr@Base 2.5.1
  wtap_get_bytes_dumped@Base 1.9.1
  wtap_get_debug_if_descr@Base 1.99.9
diff --git a/file.c b/file.c
index 6d95766040..a94ecd5eff 100644
--- a/file.c
+++ b/file.c
@@ -1023,6 +1023,52 @@ cf_get_display_name(capture_file *cf)
   return displayname;
 }
 
+gchar *
+cf_get_basename(capture_file *cf)
+{
+  gchar *displayname;
+
+  /* Return a name to use in the GUI for the basename for files to
+     which we save statistics */
+  if (!cf->is_tempfile) {
+    /* Get the last component of the file name, and use that. */
+    if (cf->filename) {
+      displayname = g_filename_display_basename(cf->filename);
+
+      /* If the file name ends with any extension that corresponds
+         to a file type we support - including compressed versions
+         of those files - strip it off. */
+      size_t displayname_len = strlen(displayname);
+      GSList *extensions = wtap_get_all_file_extensions_list();
+      GSList *suffix;
+      for (suffix = extensions; suffix != NULL; suffix = g_slist_next(suffix)) {
+        /* Does the file name end with that extension? */
+        const char *extension = (char *)suffix->data;
+        size_t extension_len = strlen(extension);
+        if (displayname_len > extension_len &&
+          displayname[displayname_len - extension_len - 1] == '.' &&
+          strcmp(&displayname[displayname_len - extension_len], extension) == 0) {
+            /* Yes.  Strip the extension off, and return the result. */
+            displayname[displayname_len - extension_len - 1] = '\0';
+            return displayname;
+        }
+      }
+    } else {
+      displayname=g_strdup("");
+    }
+  } else {
+    /* The file we read is a temporary file from a live capture or
+       a merge operation; we don't mention its name, but, if it's
+       from a capture, give the source of the capture. */
+    if (cf->source) {
+      displayname = g_strdup(cf->source);
+    } else {
+      displayname = g_strdup("");
+    }
+  }
+  return displayname;
+}
+
 void cf_set_tempfile_source(capture_file *cf, gchar *source) {
   if (cf->source) {
     g_free(cf->source);
diff --git a/file.h b/file.h
index 3088435a60..090528654b 100644
--- a/file.h
+++ b/file.h
@@ -275,6 +275,17 @@ cf_write_status_t cf_export_specified_packets(capture_file *cf,
  */
 gchar *cf_get_display_name(capture_file *cf);
 
+/**
+ * Get a name that can be used to generate a file name from the
+ * capture file name.  It's based on the displayable name, so it's
+ * UTF-8; if it ends with a suffix that's used by a file type libwiretap
+ * can read, we strip that suffix off.
+ *
+ * @param cf the capture file
+ * @return the base name (must be g_free'd)
+ */
+gchar *cf_get_basename(capture_file *cf);
+
 /**
  * Set the source of the capture data for temporary files, e.g.
  * "Interface eth0" or "Pipe from Pong"
diff --git a/ui/qt/capture_file.cpp b/ui/qt/capture_file.cpp
index 3aee4f557c..039ded83aa 100644
--- a/ui/qt/capture_file.cpp
+++ b/ui/qt/capture_file.cpp
@@ -160,16 +160,15 @@ const QString CaptureFile::fileName()
 
 const QString CaptureFile::fileBaseName()
 {
-    QString path, baseName;
+    QString baseName;
 
-    path = filePath();
-    if (!path.isEmpty()) {
-        QFileInfo cfi(path);
-        baseName = cfi.baseName();
+    if (isValid()) {
+        char *basename = cf_get_basename(cap_file_);
+        baseName = basename;
+        g_free(basename);
     } else {
         baseName = QString();
     }
-
     return baseName;
 }
 
diff --git a/wiretap/file_access.c b/wiretap/file_access.c
index cc29ed8eb7..5de6744e3a 100644
--- a/wiretap/file_access.c
+++ b/wiretap/file_access.c
@@ -1635,7 +1635,7 @@ static const struct file_type_subtype_info* dump_open_table = dump_open_table_ba
  * to the number of elements in the static table, but, if we have to
  * allocate the GArray, it's changed to have the size of the GArray.
  */
-gint wtap_num_file_types_subtypes = sizeof(dump_open_table_base) / sizeof(struct file_type_subtype_info);
+static gint wtap_num_file_types_subtypes = sizeof(dump_open_table_base) / sizeof(struct file_type_subtype_info);
 
 /*
  * Pointer to the GArray; NULL until it's needed.
@@ -2025,11 +2025,13 @@ add_extensions_for_file_type_subtype(int file_type_subtype, GSList *extensions,
 
 	/*
 	 * Add the default extension, and all compressed variants of
-	 * it.
+	 * it, if there is a default extension.
 	 */
-	extensions = add_extensions(extensions,
-	    dump_open_table[file_type_subtype].default_file_extension,
-	    compressed_file_extensions);
+	if (dump_open_table[file_type_subtype].default_file_extension != NULL) {
+		extensions = add_extensions(extensions,
+		    dump_open_table[file_type_subtype].default_file_extension,
+		    compressed_file_extensions);
+	}
 
 	if (dump_open_table[file_type_subtype].additional_file_extensions != NULL) {
 		/*
@@ -2095,10 +2097,37 @@ wtap_get_file_extensions_list(int file_type_subtype, gboolean include_compressed
 	return extensions;
 }
 
+/* Return a list of all extensions that are used by all file types that
+   we can read, including compressed extensions, e.g. not just "pcap" but
+   also "pcap.gz" if we can read gzipped files.
+
+   "File type" means "include file types that correspond to collections
+   of network packets, as well as file types that store data that just
+   happens to be transported over protocols such as HTTP but that aren't
+   collections of network packets, and plain text files".
+
+   All strings in the list are allocated with g_malloc() and must be freed
+   with g_free(). */
+GSList *
+wtap_get_all_file_extensions_list(void)
+{
+	GSList *extensions;
+	int i;
+
+	extensions = NULL;	/* empty list, to start with */
+
+	for (i = 0; i < WTAP_NUM_FILE_TYPES_SUBTYPES; i++) {
+		extensions = add_extensions_for_file_type_subtype(i, extensions,
+		    compressed_file_extension_table);
+	}
+
+	return extensions;
+}
+
 /*
  * Free a list returned by wtap_get_file_extension_type_extensions(),
- * wtap_get_all_capture_file_extensions_list, or
- * wtap_get_file_extensions_list().
+ * wtap_get_all_capture_file_extensions_list, wtap_get_file_extensions_list(),
+ * or wtap_get_all_file_extensions_list().
  */
 void
 wtap_free_extensions_list(GSList *extensions)
diff --git a/wiretap/wtap.h b/wiretap/wtap.h
index ceedb762a8..d1beb85dfe 100644
--- a/wiretap/wtap.h
+++ b/wiretap/wtap.h
@@ -2004,6 +2004,8 @@ const char *wtap_default_file_extension(int filetype);
 WS_DLL_PUBLIC
 GSList *wtap_get_file_extensions_list(int filetype, gboolean include_compressed);
 WS_DLL_PUBLIC
+GSList *wtap_get_all_file_extensions_list(void);
+WS_DLL_PUBLIC
 void wtap_free_extensions_list(GSList *extensions);
 
 WS_DLL_PUBLIC