diff --git a/src/applications/differential/parser/DifferentialChangesetParser.php b/src/applications/differential/parser/DifferentialChangesetParser.php
--- a/src/applications/differential/parser/DifferentialChangesetParser.php
+++ b/src/applications/differential/parser/DifferentialChangesetParser.php
@@ -1347,12 +1347,10 @@
       $copies = array();
       foreach ($changeset->getHunks() as $hunk) {
         $added = $hunk->getStructuredNewFile();
+        $atype = array();
 
         foreach ($added as $line => $info) {
-          if ($info['type'] != '+') {
-            unset($added[$line]);
-            continue;
-          }
+          $atype[$line] = $info['type'];
           $added[$line] = trim($info['text']);
         }
 
@@ -1365,6 +1363,12 @@
             continue;
           }
 
+          if ($atype[$line] !== '+') {
+            // This line hasn't been changed in the new file, so don't try
+            // to figure out where it came from.
+            continue;
+          }
+
           if (empty($map[$code])) {
             // This line was too short to trigger copy/move detection.
             continue;
diff --git a/src/applications/differential/storage/__tests__/DifferentialDiffTestCase.php b/src/applications/differential/storage/__tests__/DifferentialDiffTestCase.php
--- a/src/applications/differential/storage/__tests__/DifferentialDiffTestCase.php
+++ b/src/applications/differential/storage/__tests__/DifferentialDiffTestCase.php
@@ -3,17 +3,36 @@
 final class DifferentialDiffTestCase extends ArcanistPhutilTestCase {
 
   public function testDetectCopiedCode() {
+    $copies = $this->detectCopiesIn('lint_engine.diff');
+
+    $this->assertEqual(
+      array_combine(range(237, 252), range(167, 182)),
+      ipull($copies, 1));
+  }
+
+  public function testDetectCopiedOverlaidCode() {
+    $copies = $this->detectCopiesIn('copy_overlay.diff');
+
+    $this->assertEqual(
+      array(
+        7 => 22,
+        8 => 23,
+        9 => 24,
+        10 => 25,
+        11 => 26,
+        12 => 27,
+      ),
+      ipull($copies, 1));
+  }
+
+  private function detectCopiesIn($file) {
     $root = dirname(__FILE__).'/diff/';
     $parser = new ArcanistDiffParser();
 
     $diff = DifferentialDiff::newFromRawChanges(
       PhabricatorUser::getOmnipotentUser(),
-      $parser->parseDiff(Filesystem::readFile($root.'lint_engine.diff')));
-    $copies = idx(head($diff->getChangesets())->getMetadata(), 'copy:lines');
-
-    $this->assertEqual(
-      array_combine(range(237, 252), range(167, 182)),
-      ipull($copies, 1));
+      $parser->parseDiff(Filesystem::readFile($root.$file)));
+    return idx(head($diff->getChangesets())->getMetadata(), 'copy:lines');
   }
 
   public function testDetectSlowCopiedCode() {
diff --git a/src/applications/differential/storage/__tests__/diff/copy_overlay.diff b/src/applications/differential/storage/__tests__/diff/copy_overlay.diff
new file mode 100644
--- /dev/null
+++ b/src/applications/differential/storage/__tests__/diff/copy_overlay.diff
@@ -0,0 +1,41 @@
+diff --git a/test.c b/test.c
+index 441f670..5a0aa05 100644
+--- a/test.c
++++ b/test.c
+@@ -1,33 +1,28 @@
+ // NOTE: Lines must be more than 30 characters long to activate copy/move
+ // detection.
+
+ if (100000000000000000000000000000)
+ {
+   // A
+   // B
+ }
+-else if (200000000000000000000000000000)
++else if (500000000000000000000000000000)
+ {
+-  // C
+-  // D
++  // I
++  // J
+ }
+ else if (300000000000000000000000000000)
+ {
+   // E
+   // F
+ }
+ else if (400000000000000000000000000000)
+ {
+   // G
+   // H
+ }
+-else if (500000000000000000000000000000)
+-{
+-  // I
+-  // J
+-}
+ else if (600000000000000000000000000000)
+ {
+   // K
+   // L
+ }