diff --git a/newsfragments/740.bugfix b/newsfragments/740.bugfix
new file mode 100644
index 000000000..93337e3d6
--- /dev/null
+++ b/newsfragments/740.bugfix
@@ -0,0 +1,2 @@
+``FormatMRC``: relax restrictive check on the overloaded MZ header
+value, which caused failures to read files where MZ == 1
diff --git a/src/dxtbx/format/FormatMRC.py b/src/dxtbx/format/FormatMRC.py
index 4b84858a5..9eefb2fef 100644
--- a/src/dxtbx/format/FormatMRC.py
+++ b/src/dxtbx/format/FormatMRC.py
@@ -63,9 +63,12 @@ def _unpack_header(header):
 
         # For image stacks, NX==MX etc. should always be true. Assert this
         # to ensure we fail on an MRC file of the wrong type.
-        assert hd["nx"] == hd["mx"]
-        assert hd["ny"] == hd["my"]
-        assert hd["nz"] == hd["mz"]
+        try:
+            assert hd["nx"] == hd["mx"]
+            assert hd["ny"] == hd["my"]
+            assert (hd["nz"] == hd["mz"]) or (hd["mz"] == 1)
+        except AssertionError:
+            raise ValueError("Unexpected data size values in the header")
 
         return hd