diff --git a/Modules/zipimport.c b/Modules/zipimport.c
index 68c2894fbe1..11c39045253 100644
--- a/Modules/zipimport.c
+++ b/Modules/zipimport.c
@@ -736,7 +736,8 @@ read_directory(PyObject *archive_obj)
 
     fp = _Py_fopen(archive_obj, "rb");
     if (fp == NULL) {
-        PyErr_Format(ZipImportError, "can't open Zip file: '%U'", archive_obj);
+        if (!PyErr_Occurred())
+            PyErr_Format(ZipImportError, "can't open Zip file: '%U'", archive_obj);
         return NULL;
     }
     fseek(fp, -22, SEEK_END);
@@ -909,8 +910,9 @@ get_data(PyObject *archive, PyObject *toc_entry)
 
     fp = _Py_fopen(archive, "rb");
     if (!fp) {
-        PyErr_Format(PyExc_IOError,
-           "zipimport: can not open file %U", archive);
+        if (!PyErr_Occurred())
+            PyErr_Format(PyExc_IOError,
+               "zipimport: can not open file %U", archive);
         return NULL;
     }