diff --git a/Lib/gzip.py b/Lib/gzip.py
index 5bcfe61..b6656a9 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -413,8 +413,10 @@
             if self.fileobj is None:
                 return b''
             try:
-                # 1024 is the same buffering heuristic used in read()
-                self._read(max(n, 1024))
+                # Ensure that we don't return b"" if we haven't reached EOF.
+                while self.extrasize == 0:
+                    # 1024 is the same buffering heuristic used in read()
+                    self._read(max(n, 1024))
             except EOFError:
                 pass
         offset = self.offset - self.extrastart
diff --git a/Misc/NEWS b/Misc/NEWS
index 92a4d79..53f62a0 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -81,8 +81,8 @@
   constructor, objects in the ipaddress module no longer implement __index__
   (they still implement __int__ as appropriate)
 
-- Issue #15546: Fix handling of pathological input data in the read1() method of
-  the BZ2File, GzipFile and LZMAFile classes.
+- Issue #15546: Fix handling of pathological input data in the peek() and
+  read1() methods of the BZ2File, GzipFile and LZMAFile classes.
 
 - Issue #13052: Fix IDLE crashing when replace string in Search/Replace dialog
   ended with '\'. Patch by Roger Serwy.