diff --git a/lib/src/reader.dart b/lib/src/reader.dart
index f4b356f..eff4135 100644
--- a/lib/src/reader.dart
+++ b/lib/src/reader.dart
@@ -309,15 +309,20 @@
     return size;
   }
 
+  /// Ater we detected the end of a tar file, optionally check for trailing
+  /// data.
   Future<void> _handleExpectedEof() async {
     if (_checkNoTrailingData) {
-      // This will be empty iff the stream is done
-      final furtherData = await _chunkedStream.read(1);
-
-      // Note that throwing will automatically cancel the reader
-      if (furtherData.isNotEmpty) {
-        throw TarException('Illegal content after the end of the tar archive.');
-      }
+      // Trailing zeroes are okay, but don't allow any more data here.
+      Uint8List block;
+      do {
+        block = await _chunkedStream.readBytes(blockSize);
+        if (!block.isAllZeroes) {
+          throw TarException(
+              'Illegal content after the end of the tar archive.');
+        }
+      } while (block.length == blockSize);
+      // The stream is done when we couldn't read the full block.
     }
 
     await cancel();
diff --git a/reference/pub/pana-0.12.19.tar.gz b/reference/pub/pana-0.12.19.tar.gz
new file mode 100644
index 0000000..dfb2aae
--- /dev/null
+++ b/reference/pub/pana-0.12.19.tar.gz
Binary files differ
diff --git a/test/pub_test.dart b/test/pub_test.dart
index 6cb7e70..756ee09 100644
--- a/test/pub_test.dart
+++ b/test/pub_test.dart
@@ -11,17 +11,18 @@
 void main() {
   const onceBroken = [
     'access_settings_menu-0.0.1',
+    'pana-0.12.19',
     'RAL-1.28.0',
     'rikulo_commons-0.7.6',
   ];
 
   for (final package in onceBroken) {
-    test('can read $package', () {
+    test('can read $package', () async {
       final file = File('reference/pub/$package.tar.gz');
       final tarStream = file.openRead().transform(gzip.decoder);
-      return TarReader.forEach(tarStream, (entry) {
-        // do nothing, we just want to make sure that the package can be read.
-      });
+
+      final reader = TarReader(tarStream, disallowTrailingData: true);
+      while (await reader.moveNext()) {}
     });
   }
 }
diff --git a/test/reader_test.dart b/test/reader_test.dart
index a1e2ba4..04a0572 100644
--- a/test/reader_test.dart
+++ b/test/reader_test.dart
@@ -135,7 +135,12 @@
       final input = StreamController<Uint8List>()
         ..add(emptyBlock)
         ..add(emptyBlock)
-        ..add(Uint8List(1)); // illegal content after end marker
+        // illegal content after end marker
+        ..add(Uint8List.fromList([0, 1, 2, 3]));
+
+      // The reader checks for empty data in chunks, so we timeout if the stream
+      // goes stale.
+      Timer.run(input.close);
 
       final reader = TarReader(input.stream, disallowTrailingData: true);
       await expectLater(reader.moveNext(), throwsA(isA<TarException>()));
@@ -153,6 +158,17 @@
       expectLater(reader.moveNext(), completion(isFalse));
     });
 
+    test('does not throw or cancel when there are many empty blocks', () {
+      final input = StreamController<Uint8List>();
+      for (var i = 0; i < 100; i++) {
+        input.add(emptyBlock);
+      }
+      closeLater(input);
+
+      final reader = TarReader(input.stream, disallowTrailingData: true);
+      expectLater(reader.moveNext(), completion(isFalse));
+    });
+
     test('does not throw or cancel if the stream ends without marker', () {
       final input = StreamController<Uint8List>();
       closeLater(input);