--- a/crossenv/__init__.py
+++ b/crossenv/__init__.py
@@ -707,6 +707,7 @@
         # Also: 'stdlib' might not be accurate if build-python is in a build
         # directory.
         stdlib = os.path.abspath(os.path.dirname(os.__file__))
+        build_site_dir = os.path.join(context.build_env_dir, 'lib', pyver, 'site-packages')
 
         # In python 3.11, the import machinery imports from math, which breaks
         # in our cross environment.. so we inject lib-dynload to the path also
--- a/crossenv/scripts/pywrapper.py.tmpl
+++ b/crossenv/scripts/pywrapper.py.tmpl
@@ -17,7 +17,7 @@
 os.environ['_PYTHON_SYSCONFIGDATA_NAME']={{repr(sysconfig_name)}}
 os.environ['PYTHONHOME']={{repr(self.host_home)}}
 oldpath = os.environ.get('PYTHONPATH')
-newpath = os.pathsep.join([{{repr(context.lib_path)}}, {{repr(stdlib)}}, {{repr(dynload)}}])
+newpath = os.pathsep.join([{{repr(context.lib_path)}}, {{repr(build_site_dir)}}, {{repr(stdlib)}}, {{repr(dynload)}}])
 if oldpath:
     path = os.pathsep.join([newpath, oldpath])
 else: