diff --git a/src/panfrost/bifrost/bi_opt_copy_prop.c b/src/panfrost/bifrost/bi_opt_copy_prop.c
index 4601e1230f6..06b0e41e82f 100644
--- a/src/panfrost/bifrost/bi_opt_copy_prop.c
+++ b/src/panfrost/bifrost/bi_opt_copy_prop.c
@@ -40,16 +40,26 @@ bi_word_node(bi_index idx)
         return (idx.value << 2) | idx.offset;
 }
 
-bool
+void
 bi_opt_copy_prop(bi_context *ctx)
 {
-        bool progress = false;
-
         bi_index *replacement = calloc(sizeof(bi_index), ((ctx->ssa_alloc + 1) << 2));
 
         bi_foreach_instr_global_safe(ctx, ins) {
-                if (bi_is_copy(ins))
-                        replacement[bi_word_node(ins->dest[0])] = ins->src[0];
+                if (bi_is_copy(ins)) {
+                        bi_index replace = ins->src[0];
+
+                        /* Peek through one layer so copyprop converges in one
+                         * iteration for chained moves */
+                        if (bi_is_ssa(replace)) {
+                                bi_index chained = replacement[bi_word_node(replace)];
+
+                                if (!bi_is_null(chained))
+                                        replace = chained;
+                        }
+
+                        replacement[bi_word_node(ins->dest[0])] = replace;
+                }
 
                 bi_foreach_src(ins, s) {
                         bi_index use = ins->src[s];
@@ -65,5 +75,4 @@ bi_opt_copy_prop(bi_context *ctx)
         }
 
         free(replacement);
-        return progress;
 }
diff --git a/src/panfrost/bifrost/bifrost_compile.c b/src/panfrost/bifrost/bifrost_compile.c
index dec42ca8a99..26ed1b53d1e 100644
--- a/src/panfrost/bifrost/bifrost_compile.c
+++ b/src/panfrost/bifrost/bifrost_compile.c
@@ -3035,13 +3035,13 @@ bifrost_compile_shader_nir(nir_shader *nir,
 
         /* Runs before copy prop */
         bi_opt_push_ubo(ctx);
+        bi_opt_copy_prop(ctx);
 
         bool progress = false;
 
         do {
                 progress = false;
 
-                progress |= bi_opt_copy_prop(ctx);
                 progress |= bi_opt_dead_code_eliminate(ctx, false);
         } while(progress);
 
diff --git a/src/panfrost/bifrost/compiler.h b/src/panfrost/bifrost/compiler.h
index 04b69339bda..d082a09949d 100644
--- a/src/panfrost/bifrost/compiler.h
+++ b/src/panfrost/bifrost/compiler.h
@@ -744,7 +744,7 @@ void bi_print_shader(bi_context *ctx, FILE *fp);
 
 /* BIR passes */
 
-bool bi_opt_copy_prop(bi_context *ctx);
+void bi_opt_copy_prop(bi_context *ctx);
 bool bi_opt_dead_code_eliminate(bi_context *ctx, bool soft);
 void bi_opt_push_ubo(bi_context *ctx);
 void bi_schedule(bi_context *ctx);