diff --git a/Src/Base/AMReX_CArena.cpp b/Src/Base/AMReX_CArena.cpp
index c47f8f5ed2..42987f47a8 100644
--- a/Src/Base/AMReX_CArena.cpp
+++ b/Src/Base/AMReX_CArena.cpp
@@ -2,6 +2,7 @@
 #include <AMReX_CArena.H>
 #include <AMReX_BLassert.H>
 #include <AMReX_Gpu.H>
+#include <AMReX_MFIter.H>
 #include <AMReX_ParallelReduce.H>
 
 #ifdef AMREX_TINY_PROFILING
@@ -57,7 +58,11 @@ CArena::alloc_protected (std::size_t nbytes)
     }
 #endif
 
-    if (static_cast<Long>(m_used+nbytes) >= arena_info.release_threshold) {
+    if (static_cast<Long>(m_used+nbytes) >= arena_info.release_threshold
+#ifdef AMREX_USE_GPU
+        && (MFIter::currentDepth() == 0)
+#endif
+        ) {
         freeUnused_protected();
     }
 
@@ -393,7 +398,11 @@ CArena::hasFreeDeviceMemory (std::size_t sz)
 
         std::size_t nbytes = Arena::align(sz == 0 ? 1 : sz);
 
-        if (static_cast<Long>(m_used+nbytes) >= arena_info.release_threshold) {
+        if (static_cast<Long>(m_used+nbytes) >= arena_info.release_threshold
+#ifdef AMREX_USE_GPU
+            && (MFIter::currentDepth() == 0)
+#endif
+            ) {
             freeUnused_protected();
         }
 
diff --git a/Src/Base/AMReX_MFIter.H b/Src/Base/AMReX_MFIter.H
index 7f0ca4d353..fd21b0ee7c 100644
--- a/Src/Base/AMReX_MFIter.H
+++ b/Src/Base/AMReX_MFIter.H
@@ -167,6 +167,8 @@ public:
 
     static int allowMultipleMFIters (int allow);
 
+    static int currentDepth ();
+
     void Finalize ();
 
 protected:
diff --git a/Src/Base/AMReX_MFIter.cpp b/Src/Base/AMReX_MFIter.cpp
index f68ab9ce35..6eff80f6e7 100644
--- a/Src/Base/AMReX_MFIter.cpp
+++ b/Src/Base/AMReX_MFIter.cpp
@@ -17,6 +17,16 @@ MFIter::allowMultipleMFIters (int allow)
     return allow;
 }
 
+int
+MFIter::currentDepth ()
+{
+#ifdef AMREX_USE_OMP
+#pragma omp atomic read
+#endif
+    int r = MFIter::depth;
+    return r;
+}
+
 MFIter::MFIter (const FabArrayBase& fabarray_,
                 unsigned char       flags_)
     :
@@ -222,13 +232,6 @@ MFIter::Finalize ()
     // mark as invalid
     currentIndex = endIndex;
 
-#ifdef AMREX_USE_OMP
-#pragma omp master
-#endif
-    {
-        depth = 0;
-    }
-
 #ifdef BL_USE_TEAM
     if ( ! (flags & NoTeamBarrier) )
         ParallelDescriptor::MyTeam().MemoryBarrier();
@@ -257,6 +260,13 @@ MFIter::Finalize ()
     if (m_fa) {
         m_fa.reset(nullptr);
     }
+
+#ifdef AMREX_USE_OMP
+#pragma omp single
+#endif
+    {
+        depth = 0;
+    }
 }
 
 void