diff --git a/opal/mca/hwloc/base/hwloc_base_open.c b/opal/mca/hwloc/base/hwloc_base_open.c
index 39b9d167e0..c8450d0c1b 100644
--- a/opal/mca/hwloc/base/hwloc_base_open.c
+++ b/opal/mca/hwloc/base/hwloc_base_open.c
@@ -157,10 +157,8 @@ int opal_hwloc_base_open(void)
             /* mark that no binding policy was specified */
             opal_hwloc_binding_policy &= ~OPAL_BIND_GIVEN;
         } else if (0 == strncasecmp(str_value, "none", strlen("none"))) {
-            opal_hwloc_binding_policy = OPAL_BIND_TO_NONE;
-            opal_hwloc_binding_policy |= OPAL_BIND_GIVEN;
+            OPAL_SET_BINDING_POLICY(opal_hwloc_binding_policy, OPAL_BIND_TO_NONE);
         } else {
-            opal_hwloc_binding_policy |= OPAL_BIND_GIVEN;
             tmpvals = opal_argv_split(str_value, ':');
             if (1 < opal_argv_count(tmpvals)) {
                 quals = opal_argv_split(tmpvals[1], ',');
@@ -217,7 +215,6 @@ int opal_hwloc_base_open(void)
                 return OPAL_ERR_BAD_PARAM;
             }
             OPAL_SET_BINDING_POLICY(opal_hwloc_binding_policy, OPAL_BIND_TO_CORE);
-            opal_hwloc_binding_policy |= OPAL_BIND_GIVEN;
         }
 
         mca_base_param_reg_int_name("hwloc", "base_bind_to_socket",
@@ -233,7 +230,6 @@ int opal_hwloc_base_open(void)
                 return OPAL_ERR_SILENT;
             }
             OPAL_SET_BINDING_POLICY(opal_hwloc_binding_policy, OPAL_BIND_TO_SOCKET);
-            opal_hwloc_binding_policy |= OPAL_BIND_GIVEN;
         }
 
         mca_base_param_reg_int_name("hwloc", "base_report_bindings",
@@ -253,7 +249,6 @@ int opal_hwloc_base_open(void)
                 return OPAL_ERR_SILENT;
             }
             OPAL_SET_BINDING_POLICY(opal_hwloc_binding_policy, OPAL_BIND_TO_CPUSET);
-            opal_hwloc_binding_policy |= OPAL_BIND_GIVEN;
         }
 
         /* cpu allocation specification */
@@ -267,7 +262,6 @@ int opal_hwloc_base_open(void)
                  * ignored if someone didn't also specify a binding policy
                  */
                 OPAL_SET_BINDING_POLICY(opal_hwloc_binding_policy, OPAL_BIND_TO_CPUSET);
-                opal_hwloc_binding_policy |= OPAL_BIND_GIVEN;
             }
         }
 
diff --git a/opal/mca/hwloc/base/hwloc_base_util.c b/opal/mca/hwloc/base/hwloc_base_util.c
index 9d4a35ea6a..faeff3b121 100644
--- a/opal/mca/hwloc/base/hwloc_base_util.c
+++ b/opal/mca/hwloc/base/hwloc_base_util.c
@@ -1697,7 +1697,12 @@ static int build_map(int *num_sockets_arg, int *num_cores_arg,
        to look this up every time) */
     if (num_sockets < 0) {
         num_sockets = hwloc_get_nbobjs_by_type(opal_hwloc_topology, HWLOC_OBJ_SOCKET);
-
+        /* some systems (like the iMac) only have one
+         * socket and so don't report a socket
+         */
+        if (0 == num_sockets) {
+            num_sockets = 1;
+        }
         /* Lazy: take the total number of cores that we have in the
            topology; that'll be more than the max number of cores
            under any given socket */
diff --git a/opal/mca/hwloc/hwloc.h b/opal/mca/hwloc/hwloc.h
index 81be583c07..5eadaa7199 100644
--- a/opal/mca/hwloc/hwloc.h
+++ b/opal/mca/hwloc/hwloc.h
@@ -204,7 +204,7 @@ typedef uint16_t opal_binding_policy_t;
 #define OPAL_GET_BINDING_POLICY(pol) \
     ((pol) & 0x0fff)
 #define OPAL_SET_BINDING_POLICY(target, pol) \
-    (target) = (pol) | ((target) & 0xf000)
+    (target) = (pol) | (((target) & 0xf000) | OPAL_BIND_GIVEN)
 /* check if policy is set */
 #define OPAL_BINDING_POLICY_IS_SET(pol) \
     ((pol) & 0x4000)