diff --git a/src/c3nav/editor/api.py b/src/c3nav/editor/api.py
index 90472968..72bc3384 100644
--- a/src/c3nav/editor/api.py
+++ b/src/c3nav/editor/api.py
@@ -24,8 +24,6 @@ class EditorViewSet(ViewSet):
         for space in spaces.values():
             if space.outside:
                 space.geometry = space.geometry.difference(buildings_geom)
-            else:
-                space.geometry = space.geometry.intersection(buildings_geom)
             columns_geom = cascaded_union([column.geometry for column in space.columns.all()])
             space.geometry = space.geometry.difference(columns_geom)
             space_holes_geom = cascaded_union([hole.geometry for hole in space.holes.all()])
@@ -103,7 +101,6 @@ class EditorViewSet(ViewSet):
                     other_space.geometry = other_space.geometry.difference(buildings_geom)
                     other_space.color = 'rgba(255, 255, 255, 0.7)'
                 else:
-                    other_space.geometry = other_space.geometry.intersection(buildings_geom)
                     other_space.color = 'rgba(255, 255, 255, 0.3)'
 
             results = chain(
diff --git a/src/c3nav/mapdata/migrations/0011_outside_only_outside.py b/src/c3nav/mapdata/migrations/0011_outside_only_outside.py
new file mode 100644
index 00000000..72270f04
--- /dev/null
+++ b/src/c3nav/mapdata/migrations/0011_outside_only_outside.py
@@ -0,0 +1,27 @@
+# -*- coding: utf-8 -*-
+# Generated by Django 1.11.2 on 2017-06-11 11:17
+from __future__ import unicode_literals
+
+from django.db import migrations, models
+
+
+def secondary_level_spaces_inside(apps, schema_editor):
+    Space = apps.get_model('mapdata', 'Space')
+    Space.objects.filter(section__on_top_of__isnull=False).update(outside=False)
+
+
+
+class Migration(migrations.Migration):
+
+    dependencies = [
+        ('mapdata', '0010_on_top_of'),
+    ]
+
+    operations = [
+        migrations.AlterField(
+            model_name='space',
+            name='outside',
+            field=models.BooleanField(default=False, verbose_name='only outside of building'),
+        ),
+        migrations.RunPython(secondary_level_spaces_inside),
+    ]
diff --git a/src/c3nav/mapdata/models/geometry/section.py b/src/c3nav/mapdata/models/geometry/section.py
index 56817d91..be6d61d1 100644
--- a/src/c3nav/mapdata/models/geometry/section.py
+++ b/src/c3nav/mapdata/models/geometry/section.py
@@ -54,7 +54,7 @@ class Space(SpecificLocation, SectionGeometryMixin, models.Model):
     )
     geometry = GeometryField('polygon')
     category = models.CharField(verbose_name=_('category'), choices=CATEGORIES, default='normal', max_length=16)
-    outside = models.BooleanField(default=False, verbose_name=_('is outside of building'))
+    outside = models.BooleanField(default=False, verbose_name=_('only outside of building'))
 
     class Meta:
         verbose_name = _('Space')