diff --git a/etiquette/photodb.py b/etiquette/photodb.py
index 00f91ab..0eedaec 100644
--- a/etiquette/photodb.py
+++ b/etiquette/photodb.py
@@ -530,7 +530,7 @@ class PDBPhotoMixin:
             }
             yield parameters
 
-        photo_tag_rel_intersections = searchhelpers.photo_tag_rel_intersections(
+        photo_tag_rel_exist_clauses = searchhelpers.photo_tag_rel_exist_clauses(
             tag_musts,
             tag_mays,
             tag_forbids,
@@ -594,17 +594,10 @@ class PDBPhotoMixin:
         for (column, value) in maximums.items():
             wheres.append(column + ' <= ' + str(value))
 
-        # In order to use ORDER BY RANDOM(), we must place all of the intersect
-        # tag searches into a subquery. If we simply try to do
-        # SELECT * ... INTERSECT SELECT * ... ORDER BY RANDOM()
-        # we get an error that random is not a column. But placing all of the
-        # selects into a named subquery fixes that.
-        query = ['SELECT * FROM']
-        if photo_tag_rel_intersections:
-            intersections = '(%s) photos' % '\nINTERSECT\n'.join(photo_tag_rel_intersections)
-            query.append(intersections)
-        else:
-            query.append('photos')
+        if photo_tag_rel_exist_clauses:
+            wheres.extend(photo_tag_rel_exist_clauses)
+
+        query = ['SELECT * FROM photos']
 
         if wheres:
             wheres = 'WHERE ' + ' AND '.join(wheres)
diff --git a/etiquette/searchhelpers.py b/etiquette/searchhelpers.py
index 22e1599..29c703f 100644
--- a/etiquette/searchhelpers.py
+++ b/etiquette/searchhelpers.py
@@ -358,37 +358,36 @@ def normalize_tag_expression(expression):
 
     return expression
 
-INTERSECT_FORMAT = '''
-SELECT * FROM photos WHERE {operator} (
+EXIST_FORMAT = '''
+{operator} (
     SELECT 1 FROM photo_tag_rel WHERE photos.id == photo_tag_rel.photoid
     AND tagid IN {tagset}
 )
 '''.strip()
-def photo_tag_rel_intersections(tag_musts, tag_mays, tag_forbids):
+def photo_tag_rel_exist_clauses(tag_musts, tag_mays, tag_forbids):
     (tag_musts, tag_mays, tag_forbids) = expand_mmf(
         tag_musts,
         tag_mays,
         tag_forbids,
     )
 
-    intersections = []
+    clauses = []
     for tag_must_group in tag_musts:
-        intersections.append( ('EXISTS', tag_must_group) )
+        clauses.append( ('EXISTS', tag_must_group) )
     if tag_mays:
-        intersections.append( ('EXISTS', tag_mays) )
+        clauses.append( ('EXISTS', tag_mays) )
     if tag_forbids:
-        intersections.append( ('NOT EXISTS', tag_forbids) )
+        clauses.append( ('NOT EXISTS', tag_forbids) )
 
-    intersections = [
-        #(operator, helpers.sql_listify([tag.id for tag in tagset] + [""]))
+    clauses = [
         (operator, helpers.sql_listify(tag.id for tag in tagset))
-        for (operator, tagset) in intersections
+        for (operator, tagset) in clauses
     ]
-    intersections = [
-        INTERSECT_FORMAT.format(operator=operator, tagset=tagset)
-        for (operator, tagset) in intersections
+    clauses = [
+        EXIST_FORMAT.format(operator=operator, tagset=tagset)
+        for (operator, tagset) in clauses
     ]
-    return intersections
+    return clauses
 
 def normalize_tagset(photodb, tags, warning_bag=None):
     if not tags: