diff --git a/src/panfrost/bifrost/bi_helper_invocations.c b/src/panfrost/bifrost/bi_helper_invocations.c
index 564027187ea..a8d2c61c1e2 100644
--- a/src/panfrost/bifrost/bi_helper_invocations.c
+++ b/src/panfrost/bifrost/bi_helper_invocations.c
@@ -119,10 +119,6 @@ bi_block_uses_helpers(bi_block *block)
 static bool
 bi_block_terminates_helpers(bi_block *block)
 {
-        /* Can't terminate if there are no helpers */
-        if (!(block->pass_flags & 1))
-                return false;
-
         /* Can't terminate if a successor needs helpers */
         pan_foreach_successor((&block->base), succ) {
                 if (((bi_block *) succ)->pass_flags & 1)
@@ -187,19 +183,19 @@ bi_analyze_helper_terminate(bi_context *ctx)
         _mesa_set_destroy(visited, NULL);
         _mesa_set_destroy(worklist, NULL);
 
-        /* Finally, set helper_terminate on the last derivative-calculating
-         * instruction in a block that terminates helpers */
+        /* Finally, mark clauses requiring helpers */
         bi_foreach_block(ctx, _block) {
                 bi_block *block = (bi_block *) _block;
 
-                if (!bi_block_terminates_helpers(block))
-                        continue;
+                /* At the end, there are helpers iff we don't terminate */
+                bool helpers = !bi_block_terminates_helpers(block);
 
-                bi_foreach_instr_in_block_rev(block, I) {
-                        if (bi_instr_uses_helpers(I)) {
-                                I->tdd = true;
-                                break;
+                bi_foreach_clause_in_block_rev(block, clause) {
+                        bi_foreach_instr_in_clause_rev(block, clause, I) {
+                                helpers |= bi_instr_uses_helpers(I);
                         }
+
+                        clause->td = !helpers;
                 }
         }
 }
diff --git a/src/panfrost/bifrost/bi_pack.c b/src/panfrost/bifrost/bi_pack.c
index 491d71bebec..a9a1a415fd4 100644
--- a/src/panfrost/bifrost/bi_pack.c
+++ b/src/panfrost/bifrost/bi_pack.c
@@ -28,7 +28,7 @@
  * bits on the wire (as well as fixup branches) */
 
 static uint64_t
-bi_pack_header(bi_clause *clause, bi_clause *next_1, bi_clause *next_2, bool tdd)
+bi_pack_header(bi_clause *clause, bi_clause *next_1, bi_clause *next_2)
 {
         /* next_dependencies are the union of the dependencies of successors'
          * dependencies */
@@ -43,7 +43,7 @@ bi_pack_header(bi_clause *clause, bi_clause *next_1, bi_clause *next_2, bool tdd
                 .flow_control =
                         (next_1 == NULL && next_2 == NULL) ?
                         BIFROST_FLOW_END :  clause->flow_control,
-                .terminate_discarded_threads = tdd,
+                .terminate_discarded_threads = clause->td,
                 .next_clause_prefetch = clause->next_clause_prefetch && next_1,
                 .staging_barrier = staging_barrier,
                 .staging_register = clause->staging_register,
@@ -625,8 +625,7 @@ bi_pack_format(struct util_dynarray *emission,
 static void
 bi_pack_clause(bi_context *ctx, bi_clause *clause,
                 bi_clause *next_1, bi_clause *next_2,
-                struct util_dynarray *emission, gl_shader_stage stage,
-                bool tdd)
+                struct util_dynarray *emission, gl_shader_stage stage)
 {
         struct bi_packed_tuple ins[8] = { 0 };
 
@@ -644,7 +643,7 @@ bi_pack_clause(bi_context *ctx, bi_clause *clause,
         unsigned constant_quads =
                 DIV_ROUND_UP(clause->constant_count - (ec0_packed ? 1 : 0), 2);
 
-        uint64_t header = bi_pack_header(clause, next_1, next_2, tdd);
+        uint64_t header = bi_pack_header(clause, next_1, next_2);
         uint64_t ec0 = (clause->constants[0] >> 4);
         unsigned m0 = (clause->pcrel_idx == 0) ? 4 : 0;
 
@@ -739,17 +738,7 @@ bi_pack(bi_context *ctx, struct util_dynarray *emission)
 
                         previous_size = emission->size;
 
-                        /* Terminate discarded threads after the clause if any
-                         * instruction needs threads terminated. Note that this
-                         * may be set for CLPER.i32 which is not
-                         * message-passing, so we need to check all
-                         * instructions */
-                        bool tdd = false;
-
-                        bi_foreach_instr_in_clause(block, clause, I)
-                                tdd |= I->tdd;
-
-                        bi_pack_clause(ctx, clause, next, next_2, emission, ctx->stage, tdd);
+                        bi_pack_clause(ctx, clause, next, next_2, emission, ctx->stage);
 
                         if (!is_last)
                                 bi_collect_blend_ret_addr(ctx, emission, clause);
diff --git a/src/panfrost/bifrost/bi_print.c b/src/panfrost/bifrost/bi_print.c
index 295ff8efcab..aea95cc071d 100644
--- a/src/panfrost/bifrost/bi_print.c
+++ b/src/panfrost/bifrost/bi_print.c
@@ -103,6 +103,9 @@ bi_print_clause(bi_clause *clause, FILE *fp)
         if (clause->staging_barrier)
                 fprintf(fp, " osrb");
 
+        if (clause->td)
+                fprintf(fp, " td");
+
         if (clause->pcrel_idx != ~0)
                 fprintf(fp, " pcrel(%u)", clause->pcrel_idx);
 
diff --git a/src/panfrost/bifrost/bi_printer.c.py b/src/panfrost/bifrost/bi_printer.c.py
index b9450dbed0c..306124b5811 100644
--- a/src/panfrost/bifrost/bi_printer.c.py
+++ b/src/panfrost/bifrost/bi_printer.c.py
@@ -168,9 +168,6 @@ bi_print_instr(bi_instr *I, FILE *fp)
     if (I->table)
         fprintf(fp, ".%s", bi_table_as_str(I->table));
 
-    if (I->tdd)
-        fprintf(fp, ".tdd");
-
     switch (I->op) {
 % for opcode in ops:
 <%
diff --git a/src/panfrost/bifrost/bifrost_compile.c b/src/panfrost/bifrost/bifrost_compile.c
index 5d5ddfae855..3b577944a77 100644
--- a/src/panfrost/bifrost/bifrost_compile.c
+++ b/src/panfrost/bifrost/bifrost_compile.c
@@ -3585,8 +3585,9 @@ bifrost_compile_shader_nir(nir_shader *nir,
                 bi_print_shader(ctx, stdout);
         bi_lower_fau(ctx);
 
-        /* Analyze as late as possible before RA/scheduling */
-        bi_analyze_helper_terminate(ctx);
+        /* Analyze before register allocation to avoid false dependencies. The
+         * skip bit is a function of only the data flow graph and is invariant
+         * under valid scheduling. */
         bi_analyze_helper_requirements(ctx);
 
         bi_register_allocate(ctx);
@@ -3595,6 +3596,10 @@ bifrost_compile_shader_nir(nir_shader *nir,
                 bi_print_shader(ctx, stdout);
         bi_schedule(ctx);
         bi_assign_scoreboard(ctx);
+
+        /* Analyze after scheduling since we depend on instruction order. */
+        bi_analyze_helper_terminate(ctx);
+
         if (bifrost_debug & BIFROST_DBG_SHADERS && !skip_internal)
                 bi_print_shader(ctx, stdout);
 
diff --git a/src/panfrost/bifrost/compiler.h b/src/panfrost/bifrost/compiler.h
index fa20643a9d5..6966102e8aa 100644
--- a/src/panfrost/bifrost/compiler.h
+++ b/src/panfrost/bifrost/compiler.h
@@ -316,9 +316,6 @@ typedef struct {
          * useless double fills */
         bool no_spill;
 
-        /* Should we terminate discarded threads after executing this instruction? */
-        bool tdd;
-
         /* Override table, inducing a DTSEL_IMM pair if nonzero */
         enum bi_table table;
 
@@ -520,6 +517,9 @@ typedef struct {
         /* Unique in a clause */
         enum bifrost_message_type message_type;
         bi_instr *message;
+
+        /* Discard helper threads */
+        bool td;
 } bi_clause;
 
 typedef struct bi_block {