diff --git a/core/src/G3Reader.cxx b/core/src/G3Reader.cxx
index db0fceec..718c0d08 100644
--- a/core/src/G3Reader.cxx
+++ b/core/src/G3Reader.cxx
@@ -80,7 +80,7 @@ void G3Reader::Process(G3FramePtr frame, std::deque<G3FramePtr> &out)
 	if (Py_IsInitialized())
 		_save = PyEval_SaveThread();
 
-	if (stream_.peek() == EOF) {
+	while (stream_.peek() == EOF) {
 		if (filename_.size() > 0) {
 			StartFile(filename_.front());
 			filename_.pop_front();
diff --git a/core/tests/fileio.py b/core/tests/fileio.py
index 0b36de3f..72950458 100755
--- a/core/tests/fileio.py
+++ b/core/tests/fileio.py
@@ -46,7 +46,16 @@ def checkinfo(fr):
     n += 1
 pipe.Add(checkinfo)
 pipe.Run()
+assert n == 10, 'Wrong number of frames read (%d should be %d)' % (n, 10)
 
+# Skip empty files
+wr = core.G3Writer("empty.g3")
+del wr
+n = 0
+pipe = core.G3Pipeline()
+pipe.Add(core.G3Reader, filename=["empty.g3", "test.g3", "empty.g3"], track_filename=True)
+pipe.Add(checkinfo)
+pipe.Run()
 assert n == 10, 'Wrong number of frames read (%d should be %d)' % (n, 10)
 
 # Indexing