diff --git a/src/common/log.c b/src/common/log.c
index d8b0e8dd01..9807fd2921 100644
--- a/src/common/log.c
+++ b/src/common/log.c
@@ -184,7 +184,7 @@ format_msg(char *buf, size_t buf_len,
  * message.  The actual message is derived as from tor_snprintf(format,ap).
  */
 static void
-logv(int severity, unsigned int domain, const char *funcname, const char *format,
+logv(int severity, uint32_t domain, const char *funcname, const char *format,
      va_list ap)
 {
   char buf[10024];
@@ -234,7 +234,7 @@ logv(int severity, unsigned int domain, const char *funcname, const char *format
 
 /** Output a message to the log. */
 void
-_log(int severity, unsigned int domain, const char *format, ...)
+_log(int severity, uint32_t domain, const char *format, ...)
 {
   va_list ap;
   va_start(ap,format);
@@ -245,7 +245,7 @@ _log(int severity, unsigned int domain, const char *format, ...)
 /** Output a message to the log, prefixed with a function name <b>fn</b>. */
 #ifdef __GNUC__
 void
-_log_fn(int severity, unsigned int domain, const char *fn, const char *format, ...)
+_log_fn(int severity, uint32_t domain, const char *fn, const char *format, ...)
 {
   va_list ap;
   va_start(ap,format);
@@ -255,7 +255,7 @@ _log_fn(int severity, unsigned int domain, const char *fn, const char *format, .
 #else
 const char *_log_fn_function_name=NULL;
 void
-_log_fn(int severity, unsigned int domain, const char *format, ...)
+_log_fn(int severity, uint32_t domain, const char *format, ...)
 {
   va_list ap;
   va_start(ap,format);
@@ -264,7 +264,7 @@ _log_fn(int severity, unsigned int domain, const char *format, ...)
   _log_fn_function_name = NULL;
 }
 void
-_debug(unsigned int domain, const char *format, ...)
+_debug(uint32_t domain, const char *format, ...)
 {
   va_list ap;
   va_start(ap,format);
@@ -273,7 +273,7 @@ _debug(unsigned int domain, const char *format, ...)
   _log_fn_function_name = NULL;
 }
 void
-_info(unsigned int domain, const char *format, ...)
+_info(uint32_t domain, const char *format, ...)
 {
   va_list ap;
   va_start(ap,format);
@@ -282,7 +282,7 @@ _info(unsigned int domain, const char *format, ...)
   _log_fn_function_name = NULL;
 }
 void
-_notice(unsigned int domain, const char *format, ...)
+_notice(uint32_t domain, const char *format, ...)
 {
   va_list ap;
   va_start(ap,format);
@@ -291,7 +291,7 @@ _notice(unsigned int domain, const char *format, ...)
   _log_fn_function_name = NULL;
 }
 void
-_warn(unsigned int domain, const char *format, ...)
+_warn(uint32_t domain, const char *format, ...)
 {
   va_list ap;
   va_start(ap,format);
@@ -300,7 +300,7 @@ _warn(unsigned int domain, const char *format, ...)
   _log_fn_function_name = NULL;
 }
 void
-_err(unsigned int domain, const char *format, ...)
+_err(uint32_t domain, const char *format, ...)
 {
   va_list ap;
   va_start(ap,format);
diff --git a/src/common/log.h b/src/common/log.h
index eec031f1a0..dd7dcbd9b7 100644
--- a/src/common/log.h
+++ b/src/common/log.h
@@ -90,7 +90,7 @@
 /** Bandwidth accounting. */
 #define LD_ACCT     (1u<<17)
 
-typedef void (*log_callback)(int severity, unsigned int domain, const char *msg);
+typedef void (*log_callback)(int severity, uint32_t domain, const char *msg);
 
 int parse_log_level(const char *level);
 const char *log_level_to_string(int level);
@@ -113,11 +113,11 @@ void change_callback_log_severity(int loglevelMin, int loglevelMax,
                                   log_callback cb);
 
 /* Outputs a message to stdout */
-void _log(int severity, unsigned int domain, const char *format, ...) CHECK_PRINTF(3,4);
+void _log(int severity, uint32_t domain, const char *format, ...) CHECK_PRINTF(3,4);
 #define log _log /* hack it so we don't conflict with log() as much */
 
 #ifdef __GNUC__
-void _log_fn(int severity, unsigned int domain,
+void _log_fn(int severity, uint32_t domain,
              const char *funcname, const char *format, ...)
   CHECK_PRINTF(4,5);
 /** Log a message at level <b>severity</b>, using a pretty-printed version
@@ -137,12 +137,12 @@ void _log_fn(int severity, unsigned int domain,
 
 #else /* ! defined(__GNUC__) */
 
-void _log_fn(int severity, unsigned int domain, const char *format, ...);
-void _debug(unsigned int domain, const char *format, ...);
-void _info(unsigned int domain, const char *format, ...);
-void _notice(unsigned int domain, const char *format, ...);
-void _warn(unsigned int domain, const char *format, ...);
-void _err(unsigned int domain, const char *format, ...);
+void _log_fn(int severity, uint32_t domain, const char *format, ...);
+void _debug(uint32_t domain, const char *format, ...);
+void _info(uint32_t domain, const char *format, ...);
+void _notice(uint32_t domain, const char *format, ...);
+void _warn(uint32_t domain, const char *format, ...);
+void _err(uint32_t domain, const char *format, ...);
 
 #if defined(_MSC_VER) && _MSC_VER < 1300
 /* MSVC 6 and earlier don't have __FUNCTION__, or even __LINE__. */