diff --git a/opal/mca/hwloc/base/hwloc_base_frame.c b/opal/mca/hwloc/base/hwloc_base_frame.c
index da48d4833ec..af85a642dcd 100644
--- a/opal/mca/hwloc/base/hwloc_base_frame.c
+++ b/opal/mca/hwloc/base/hwloc_base_frame.c
@@ -3,6 +3,7 @@
  * Copyright (c) 2013-2018 Intel, Inc. All rights reserved.
  * Copyright (c) 2016-2017 Research Organization for Information Science
  *                         and Technology (RIST). All rights reserved.
+ * Copyright (c) 2019 IBM Corporation. All rights reserved.
  * $COPYRIGHT$
  *
  * Additional copyrights may follow
@@ -217,7 +218,14 @@ static int opal_hwloc_base_open(mca_base_open_flag_t flags)
          * we do bind to the given cpus if provided, otherwise this would be
          * ignored if someone didn't also specify a binding policy
          */
-        OPAL_SET_BINDING_POLICY(opal_hwloc_binding_policy, OPAL_BIND_TO_CPUSET);
+// Restoring pre ef86707fbe3392c8ed15f79cc4892f0313b409af behavior.
+// Formerly -cpu-set #,#,# along with -use_hwthread-cpus resulted
+// in the binding policy staying OPAL_BIND_TO_HWTHREAD
+// I think that should be right because I thought -cpu-set was a contraint you put
+// on another binding policy, not a binding policy in itself.
+        if (!OPAL_BINDING_POLICY_IS_SET(opal_hwloc_binding_policy)) {
+            OPAL_SET_BINDING_POLICY(opal_hwloc_binding_policy, OPAL_BIND_TO_CPUSET);
+        }
     }
 
     /* if we are binding to hwthreads, then we must use hwthreads as cpus */
diff --git a/opal/mca/hwloc/base/hwloc_base_util.c b/opal/mca/hwloc/base/hwloc_base_util.c
index d0cf6f03b1b..94c2740c50e 100644
--- a/opal/mca/hwloc/base/hwloc_base_util.c
+++ b/opal/mca/hwloc/base/hwloc_base_util.c
@@ -775,15 +775,34 @@ static hwloc_obj_t df_search(hwloc_topology_t topo,
         return found;
     }
     if (OPAL_HWLOC_AVAILABLE == rtype) {
+// The previous (3.x) code included a check for
+// available = opal_hwloc_base_get_available_cpus(topo, start)
+// and skipped objs that had hwloc_bitmap_iszero(available)
+        hwloc_obj_t root;
+        opal_hwloc_topo_data_t *rdata;
+        root = hwloc_get_root_obj(topo);
+        rdata = (opal_hwloc_topo_data_t*)root->userdata;
+        hwloc_cpuset_t constrained_cpuset;
+
+        constrained_cpuset = hwloc_bitmap_alloc();
+        if (rdata && rdata->available) {
+            hwloc_bitmap_and(constrained_cpuset, start->cpuset, rdata->available);
+        } else {
+            hwloc_bitmap_copy(constrained_cpuset, start->cpuset);
+        }
+
         unsigned idx = 0;
         if (num_objs)
-            *num_objs = hwloc_get_nbobjs_inside_cpuset_by_depth(topo, start->cpuset, search_depth);
+            *num_objs = hwloc_get_nbobjs_inside_cpuset_by_depth(topo, constrained_cpuset, search_depth);
         obj = NULL;
-        while ((obj = hwloc_get_next_obj_inside_cpuset_by_depth(topo, start->cpuset, search_depth, obj)) != NULL) {
-            if (idx == nobj)
+        while ((obj = hwloc_get_next_obj_inside_cpuset_by_depth(topo, constrained_cpuset, search_depth, obj)) != NULL) {
+            if (idx == nobj) {
+                hwloc_bitmap_free(constrained_cpuset);
                 return obj;
+            }
             idx++;
         }
+        hwloc_bitmap_free(constrained_cpuset);
         return NULL;
     }
     return NULL;
diff --git a/orte/mca/rmaps/base/rmaps_base_binding.c b/orte/mca/rmaps/base/rmaps_base_binding.c
index 0715a1fe2d8..0e80db6d483 100644
--- a/orte/mca/rmaps/base/rmaps_base_binding.c
+++ b/orte/mca/rmaps/base/rmaps_base_binding.c
@@ -16,6 +16,7 @@
  * Copyright (c) 2015-2017 Research Organization for Information Science
  *                         and Technology (RIST). All rights reserved.
  * Copyright (c) 2018      Inria.  All rights reserved.
+ * Copyright (c) 2019 IBM Corporation. All rights reserved.
  * $COPYRIGHT$
  *
  * Additional copyrights may follow
@@ -168,8 +169,19 @@ static int bind_generic(orte_job_t *jdata,
         trg_obj = NULL;
         min_bound = UINT_MAX;
         while (NULL != (tmp_obj = hwloc_get_next_obj_by_depth(node->topology->topo, target_depth, tmp_obj))) {
+            hwloc_obj_t root;
+            opal_hwloc_topo_data_t *rdata;
+            root = hwloc_get_root_obj(node->topology->topo);
+            rdata = (opal_hwloc_topo_data_t*)root->userdata;
+
             if (!hwloc_bitmap_intersects(locale->cpuset, tmp_obj->cpuset))
                 continue;
+// From the old 3.x code trg_obj was picked via a call to
+// opal_hwloc_base_find_min_bound_target_under_obj() which
+// skiped over unavailable objects (via opal_hwloc_base_get_npus).
+            if (rdata && rdata->available && !hwloc_bitmap_intersects(rdata->available, tmp_obj->cpuset))
+                continue;
+
             data = (opal_hwloc_obj_data_t*)tmp_obj->userdata;
             if (NULL == data) {
                 data = OBJ_NEW(opal_hwloc_obj_data_t);
diff --git a/orte/mca/rmaps/base/rmaps_base_ranking.c b/orte/mca/rmaps/base/rmaps_base_ranking.c
index 9c0960b93b3..175590ebb69 100644
--- a/orte/mca/rmaps/base/rmaps_base_ranking.c
+++ b/orte/mca/rmaps/base/rmaps_base_ranking.c
@@ -13,6 +13,7 @@
  * Copyright (c) 2014-2020 Intel, Inc.  All rights reserved.
  * Copyright (c) 2017      Research Organization for Information Science
  *                         and Technology (RIST). All rights reserved.
+ * Copyright (c) 2019      IBM Corporation. All rights reserved.
  * Copyright (c) 2020      Huawei Technologies Co., Ltd.  All rights reserved.
  * $COPYRIGHT$
  *
diff --git a/orte/mca/rmaps/rank_file/rmaps_rank_file_component.c b/orte/mca/rmaps/rank_file/rmaps_rank_file_component.c
index 5f7f5d66419..a3338ed09f4 100644
--- a/orte/mca/rmaps/rank_file/rmaps_rank_file_component.c
+++ b/orte/mca/rmaps/rank_file/rmaps_rank_file_component.c
@@ -15,6 +15,7 @@
  * Copyright (c) 2014-2018 Intel, Inc. All rights reserved.
  * Copyright (c) 2015      Los Alamos National Security, LLC. All rights
  *                         reserved.
+ * Copyright (c) 2019 IBM Corporation. All rights reserved.
  * $COPYRIGHT$
  *
  * Additional copyrights may follow
@@ -106,7 +107,8 @@ static int orte_rmaps_rank_file_register(void)
 static int orte_rmaps_rank_file_open(void)
 {
     /* ensure we flag mapping by user */
-    if ((NULL != opal_hwloc_base_cpu_list && !OPAL_BIND_ORDERED_REQUESTED(opal_hwloc_binding_policy)) ||
+    if ((OPAL_BIND_TO_CPUSET == OPAL_GET_BINDING_POLICY(opal_hwloc_binding_policy) &&
+        !OPAL_BIND_ORDERED_REQUESTED(opal_hwloc_binding_policy)) ||
         NULL != orte_rankfile) {
         if (ORTE_MAPPING_GIVEN & ORTE_GET_MAPPING_DIRECTIVE(orte_rmaps_base.mapping)) {
             /* if a non-default mapping is already specified, then we