diff --git a/dlls/ntdll/unix/virtual.c b/dlls/ntdll/unix/virtual.c
index 182f9089dbf..14c984b27bf 100644
--- a/dlls/ntdll/unix/virtual.c
+++ b/dlls/ntdll/unix/virtual.c
@@ -2907,7 +2907,7 @@ TEB *virtual_alloc_first_teb(void)
         exit(1);
     }
 
-    NtAllocateVirtualMemory( NtCurrentProcess(), &teb_block, 0, &total,
+    NtAllocateVirtualMemory( NtCurrentProcess(), &teb_block, is_win64 ? 0x7fffffff : 0, &total,
                              MEM_RESERVE | MEM_TOP_DOWN, PAGE_READWRITE );
     teb_block_pos = 30;
     ptr = (char *)teb_block + 30 * block_size;
@@ -2944,8 +2944,8 @@ NTSTATUS virtual_alloc_teb( TEB **ret_teb )
         {
             SIZE_T total = 32 * block_size;
 
-            if ((status = NtAllocateVirtualMemory( NtCurrentProcess(), &ptr, 0, &total,
-                                                   MEM_RESERVE, PAGE_READWRITE )))
+            if ((status = NtAllocateVirtualMemory( NtCurrentProcess(), &ptr, is_win64 ? 0x7fffffff : 0,
+                                                   &total, MEM_RESERVE, PAGE_READWRITE )))
             {
                 server_leave_uninterrupted_section( &virtual_mutex, &sigset );
                 return status;
@@ -3060,7 +3060,7 @@ NTSTATUS virtual_alloc_thread_stack( INITIAL_TEB *stack, SIZE_T reserve_size, SI
     server_enter_uninterrupted_section( &virtual_mutex, &sigset );
 
     if ((status = map_view( &view, NULL, size + extra_size, FALSE,
-                            VPROT_READ | VPROT_WRITE | VPROT_COMMITTED, 0 )) != STATUS_SUCCESS)
+                            VPROT_READ | VPROT_WRITE | VPROT_COMMITTED, 33 )) != STATUS_SUCCESS)
         goto done;
 
 #ifdef VALGRIND_STACK_REGISTER