diff --git a/if1632/kernel.spec b/if1632/kernel.spec
index be68a6ee674..7d8e9690b0c 100644
--- a/if1632/kernel.spec
+++ b/if1632/kernel.spec
@@ -6,7 +6,7 @@ file	krnl386.exe
 # present in win31, win95 and nt351
 
 1   stub FatalExit
-2   stub ExitKernel
+2   pascal16 ExitKernel() ExitKernel16
 3   pascal GetVersion() GetVersion16
 4   pascal16 LocalInit(word word word) LocalInit16
 5   register LocalAlloc(word word) WIN16_LocalAlloc
@@ -289,7 +289,7 @@ file	krnl386.exe
 348 pascal16 hmemcpy(ptr ptr long) hmemcpy16
 349 pascal   _hread(word segptr long) WIN16_hread
 350 pascal   _hwrite(word ptr long) _hwrite16
-351 stub BUNNY_351
+351 return BUNNY_351 0 0
 352 pascal   lstrcatn(segstr str word) lstrcatn16
 353 pascal   lstrcpyn(segptr str word) lstrcpyn16
 354 pascal   GetAppCompatFlags(word) GetAppCompatFlags16
@@ -370,7 +370,7 @@ file	krnl386.exe
 463 pascal SetThreadQueue(long word) SetThreadQueue16
 464 pascal GetThreadQueue(long) GetThreadQueue16
 465 stub NukeProcess
-466 stub ExitProcess
+466 pascal16 ExitProcess(word) ExitProcess16
 467 stub WOACreateConsole
 468 stub WOASpawnConApp
 469 stub WOAGimmeTitle
@@ -387,7 +387,7 @@ file	krnl386.exe
 480 pascal16 _EnterWin16Lock() SYSLEVEL_EnterWin16Lock
 481 pascal16 _LeaveWin16Lock() SYSLEVEL_LeaveWin16Lock
 482 pascal LoadSystemLibrary32(str) LoadLibrary32_16   # FIXME!
-483 stub MapProcessHandle
+483 pascal MapProcessHandle(long) MapProcessHandle
 484 pascal SetProcessDWORD(long s_word long) SetProcessDword
 485 pascal GetProcessDWORD(long s_word) GetProcessDword
 486 pascal FreeLibrary32(long) FreeLibrary
diff --git a/include/user.h b/include/user.h
index d7559270912..d74db21375c 100644
--- a/include/user.h
+++ b/include/user.h
@@ -38,7 +38,6 @@ typedef struct tagUSER_DRIVER {
 
 extern USER_DRIVER *USER_Driver;
 
-void USER_ExitWindows(void);
 WORD WINAPI UserSignalProc( UINT uCode, DWORD dwThreadOrProcessID,
                             DWORD dwFlags, HMODULE16 hModule );
 
diff --git a/include/wine/winbase16.h b/include/wine/winbase16.h
index 7097106b5f6..054d70abda3 100644
--- a/include/wine/winbase16.h
+++ b/include/wine/winbase16.h
@@ -112,6 +112,7 @@ BOOL16      WINAPI CreateDirectory16(LPCSTR,LPVOID);
 BOOL16      WINAPI DefineHandleTable16(WORD);
 ATOM        WINAPI DeleteAtom16(ATOM);
 BOOL16      WINAPI DeleteFile16(LPCSTR);
+void        WINAPI ExitKernel16(void);
 void        WINAPI FatalAppExit16(UINT16,LPCSTR);
 ATOM        WINAPI FindAtom16(SEGPTR);
 BOOL16      WINAPI FindClose16(HANDLE16);
diff --git a/loader/main.c b/loader/main.c
index 5f75eb0ab3a..a890ae06ca2 100644
--- a/loader/main.c
+++ b/loader/main.c
@@ -315,3 +315,21 @@ HINSTANCE MAIN_WinelibInit( int *argc, char *argv[] )
     return wm->module;
 }
 
+/***********************************************************************
+ *           ExitKernel16 (KERNEL.2)
+ *
+ * Clean-up everything and exit the Wine process.
+ *
+ */
+void WINAPI ExitKernel16( void )
+{
+    /* Do the clean-up stuff */
+
+    WriteOutProfiles16();
+    SHELL_SaveRegistry();
+
+    SERVICE_Exit();
+
+    exit(0);
+}
+
diff --git a/loader/task.c b/loader/task.c
index 05052e23f4e..520bf485318 100644
--- a/loader/task.c
+++ b/loader/task.c
@@ -583,8 +583,7 @@ void TASK_KillTask( HTASK16 hTask )
     if (nTaskCount <= 1)
     {
         TRACE_(task)("this is the last task, exiting\n" );
-        SERVICE_Exit();
-        USER_ExitWindows();
+        ExitKernel16();
     }
 
     /* FIXME: Hack! Send a message to the initial task so that
diff --git a/scheduler/process.c b/scheduler/process.c
index 0ffa8019e79..718fa35a55b 100644
--- a/scheduler/process.c
+++ b/scheduler/process.c
@@ -673,6 +673,14 @@ void WINAPI ExitProcess( DWORD status )
     TerminateProcess( GetCurrentProcess(), status );
 }
 
+/***********************************************************************
+ *           ExitProcess16   (KERNEL.466)
+ */
+void WINAPI ExitProcess16( WORD status )
+{
+    SYSLEVEL_ReleaseWin16Lock();
+    ExitProcess( status );
+}
 
 /******************************************************************************
  *           TerminateProcess   (KERNEL32.684)
@@ -831,6 +839,15 @@ HANDLE WINAPI OpenProcess( DWORD access, BOOL inherit, DWORD id )
     return reply.handle;
 }			      
 
+/*********************************************************************
+ *           MapProcessHandle   (KERNEL.483)
+ */
+DWORD WINAPI MapProcessHandle( HANDLE handle )
+{
+    struct get_process_info_reply reply;
+    if ( !PROCESS_QueryInfo( handle, &reply ) ) return 0;
+    return (DWORD)reply.pid;
+}
 
 /***********************************************************************
  *           GetCurrentProcessId   (KERNEL32.199)
diff --git a/windows/user.c b/windows/user.c
index abc7fd57417..4f94ec77799 100644
--- a/windows/user.c
+++ b/windows/user.c
@@ -181,24 +181,6 @@ static void USER_AppExit( HINSTANCE16 hInstance )
 }
 
 
-/***********************************************************************
- *           USER_ExitWindows
- *
- * Clean-up everything and exit the Wine process.
- * This is the back-end of ExitWindows(), called when all windows
- * have agreed to be terminated.
- */
-void USER_ExitWindows(void)
-{
-    /* Do the clean-up stuff */
-
-    WriteOutProfiles16();
-    SHELL_SaveRegistry();
-
-    exit(0);
-}
-
-
 /***********************************************************************
  *           USER_SignalProc (USER.314)
  */
@@ -329,7 +311,7 @@ BOOL WINAPI ExitWindowsEx( UINT flags, DWORD reserved )
     }
     WIN_ReleaseWinArray(list);
 
-    if (result) USER_ExitWindows();
+    if (result) ExitKernel16();
     WIN_ReleaseDesktop();
     return FALSE;
 }