diff --git a/lib/ipaddr.ml b/lib/ipaddr.ml
index e9e0409..9558641 100644
--- a/lib/ipaddr.ml
+++ b/lib/ipaddr.ml
@@ -357,7 +357,9 @@ module V4 = struct
       to_address_buffer b subnet addr;
       Buffer.contents b
 
-    let mem ip (pre,sz) = let host = 32 - sz in (ip >|> host) = (pre >|> host)
+    let mem ip (pre,sz) =
+      let m = mask sz in
+      (ip &&& m) = (pre &&& m)
 
     let subset ~subnet:(pre1,sz1) ~network:(pre2,sz2) =
       sz1 >= sz2 && mem pre1 (pre2,sz2)
diff --git a/lib_test/test_ipaddr.ml b/lib_test/test_ipaddr.ml
index 24f5921..e2697b5 100644
--- a/lib_test/test_ipaddr.ml
+++ b/lib_test/test_ipaddr.ml
@@ -305,6 +305,26 @@ module Test_v4 = struct
         (fun () -> Ipaddr_cstruct.V4.of_cstruct_exn (Cstruct.of_string addr))
     ) addrs
 
+  let test_prefix_mem () =
+    let ip = V4.of_string_exn in
+    let prefix = V4.Prefix.of_string_exn in
+    let ships = [
+      ip "10.0.0.7",            prefix "10.0.0.0/29",            true;
+      ip "172.16.255.254",      prefix "172.16.255.254/31",      true;
+      ip "192.168.0.1",         prefix "0.0.0.0/0",              true;
+      ip "192.168.0.1",         V4.Prefix.private_192,           true;
+      ip "255.255.255.255",     prefix "255.255.255.255/32",     true;
+      ip "192.0.2.1",           prefix "192.0.2.0/32",           false;
+      ip "192.0.2.1",           prefix "192.0.0.0/23",           false;
+      ip "255.255.255.255",     prefix "0.0.0.0/1",              false;
+    ] in
+    List.iter (fun (addr,subnet,is_mem) ->
+      let msg = Printf.sprintf "%s is%s in %s"
+        (V4.to_string addr) (if is_mem then "" else " not") (V4.Prefix.to_string subnet)
+      in
+      assert_equal ~msg (V4.Prefix.mem addr subnet) is_mem
+    ) ships
+
   let suite = "Test V4" >::: [
     "string_rt"            >:: test_string_rt;
     "string_rt_bad"        >:: test_string_rt_bad;
@@ -328,6 +348,7 @@ module Test_v4 = struct
     "special_addr"         >:: test_special_addr;
     "multicast_mac"        >:: test_multicast_mac;
     "domain_name"          >:: test_domain_name;
+    "prefix_mem"           >:: test_prefix_mem;
   ]
 end