#15546: Fix GzipFile.peek()'s handling of pathological input data.
This is a backport of changeset 8c07ff7f882f.
diff --git a/Lib/gzip.py b/Lib/gzip.py
index 403040b..6aacc9a 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -367,8 +367,10 @@
             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 a46bcc7..c5cbdec 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -466,6 +466,9 @@
 - Issue #15424: Add a __sizeof__ implementation for array objects.
   Patch by Ludwig Hähne.
 
+- Issue #15546: Fix handling of pathological input data in the peek() method
+  of the GzipFile class.
+
 - Issue #13052: Fix IDLE crashing when replace string in Search/Replace dialog
   ended with '\'. Patch by Roger Serwy.