diff --git a/libraries/DataFlash/DataFlash_File.cpp b/libraries/DataFlash/DataFlash_File.cpp
index c892040fd0..9576510564 100644
--- a/libraries/DataFlash/DataFlash_File.cpp
+++ b/libraries/DataFlash/DataFlash_File.cpp
@@ -417,9 +417,10 @@ bool DataFlash_File::NeedPrep()
 
 /*
   construct a log file name given a log number. 
+  The number in the log filename will *not* be zero-padded.
   Note: Caller must free.
  */
-char *DataFlash_File::_log_file_name(const uint16_t log_num) const
+char *DataFlash_File::_log_file_name_short(const uint16_t log_num) const
 {
     char *buf = nullptr;
     if (asprintf(&buf, "%s/%u.BIN", _log_directory, (unsigned)log_num) == -1) {
@@ -428,6 +429,39 @@ char *DataFlash_File::_log_file_name(const uint16_t log_num) const
     return buf;
 }
 
+/*
+  construct a log file name given a log number.
+  The number in the log filename will be zero-padded.
+  Note: Caller must free.
+ */
+char *DataFlash_File::_log_file_name_long(const uint16_t log_num) const
+{
+    char *buf = nullptr;
+    if (asprintf(&buf, "%s/%08u.BIN", _log_directory, (unsigned)log_num) == -1) {
+        return nullptr;
+    }
+    return buf;
+}
+
+/*
+  return a log filename appropriate for the supplied log_num if a
+  filename exists with the short (not-zero-padded name) then it is the
+  appropirate name, otherwise the long (zero-padded) version is.
+  Note: Caller must free.
+ */
+char *DataFlash_File::_log_file_name(const uint16_t log_num) const
+{
+    char *filename = _log_file_name_short(log_num);
+    if (filename == nullptr) {
+        return nullptr;
+    }
+    if (file_exists(filename)) {
+        return filename;
+    }
+    free(filename);
+    return _log_file_name_long(log_num);
+}
+
 /*
   return path name of the lastlog.txt marker file
   Note: Caller must free.
diff --git a/libraries/DataFlash/DataFlash_File.h b/libraries/DataFlash/DataFlash_File.h
index 585b37b981..e8a5cb750d 100644
--- a/libraries/DataFlash/DataFlash_File.h
+++ b/libraries/DataFlash/DataFlash_File.h
@@ -118,6 +118,8 @@ private:
 
     /* construct a file name given a log number. Caller must free. */
     char *_log_file_name(const uint16_t log_num) const;
+    char *_log_file_name_long(const uint16_t log_num) const;
+    char *_log_file_name_short(const uint16_t log_num) const;
     char *_lastlog_file_name() const;
     uint32_t _get_log_size(const uint16_t log_num) const;
     uint32_t _get_log_time(const uint16_t log_num) const;