diff --git a/av1/encoder/encodeframe.c b/av1/encoder/encodeframe.c
index bbd84d5d5e6c9098d680033ecdc45db1e921568d..3d2b210f04d6da8ce54a82cc450b25a3c02ed69e 100644
--- a/av1/encoder/encodeframe.c
+++ b/av1/encoder/encodeframe.c
@@ -4784,7 +4784,6 @@ static void encode_frame_internal(AV1_COMP *cpi) {
   av1_zero(rdc->comp_pred_diff);
 
 #if CONFIG_GLOBAL_MOTION
-  aom_clear_system_state();
   av1_zero(cpi->global_motion_used);
   for (i = LAST_FRAME; i <= ALTREF_FRAME; ++i) {
     set_default_gmparams(&cm->global_motion[i]);
@@ -4797,6 +4796,7 @@ static void encode_frame_internal(AV1_COMP *cpi) {
     for (frame = LAST_FRAME; frame <= ALTREF_FRAME; ++frame) {
       ref_buf = get_ref_frame_buffer(cpi, frame);
       if (ref_buf) {
+        aom_clear_system_state();
         if (compute_global_motion_feature_based(GLOBAL_TRANS_TYPES - 1,
                                                 cpi->Source, ref_buf, params)) {
           convert_model_to_params(params, &cm->global_motion[frame]);
@@ -4824,6 +4824,7 @@ static void encode_frame_internal(AV1_COMP *cpi) {
               set_default_gmparams(&cm->global_motion[frame]);
           }
         }
+        aom_clear_system_state();
       }
     }
   }
diff --git a/av1/encoder/rdopt.c b/av1/encoder/rdopt.c
index 3242f3d5495ce2b5ed9b16fd3a92d4a24053d64c..f189bd8ffef1d721a9dcd7003143340a583e97cd 100644
--- a/av1/encoder/rdopt.c
+++ b/av1/encoder/rdopt.c
@@ -4351,15 +4351,22 @@ static int get_gmbitcost(const WarpedMotionParams *gm, const aom_prob *probs) {
     case IDENTITY: bits = 0; break;
     default: assert(0); return 0;
   }
+  assert(type < GLOBAL_TRANS_TYPES);
   return bits ? (bits << AV1_PROB_COST_SHIFT) + gmtype_cost[type] : 0;
 }
 
-#define GLOBAL_MOTION_RATE(ref)                            \
-  (cpi->global_motion_used[ref] >= 2                       \
-       ? 0                                                 \
-       : get_gmbitcost(&cm->global_motion[(ref)],          \
-                       cm->fc->global_motion_types_prob) / \
-             2);
+#define GLOBAL_MOTION_COST_AMORTIZATION_BLKS 8
+
+#if GLOBAL_MOTION_COST_AMORTIZATION_BLKS > 0
+#define GLOBAL_MOTION_RATE(ref)                                         \
+  (cpi->global_motion_used[ref] >= GLOBAL_MOTION_COST_AMORTIZATION_BLKS \
+       ? 0                                                              \
+       : get_gmbitcost(&cm->global_motion[(ref)],                       \
+                       cm->fc->global_motion_types_prob) /              \
+             GLOBAL_MOTION_COST_AMORTIZATION_BLKS);
+#else
+#define GLOBAL_MOTION_RATE(ref) 0
+#endif  // GLOBAL_MOTION_COST_AMORTIZATION_BLKS > 0
 #endif  // CONFIG_GLOBAL_MOTION
 
 static int set_and_cost_bmi_mvs(const AV1_COMP *const cpi, MACROBLOCK *x,