diff --git a/common/speculative.cpp b/common/speculative.cpp
index 3e83b0964c855..41df275c9605a 100644
--- a/common/speculative.cpp
+++ b/common/speculative.cpp
@@ -311,6 +311,29 @@ llama_tokens common_speculative_gen_draft(
 
     common_sampler_reset(smpl);
 
+    // read in from an environment variable for now
+    const std::vector<float> batch_costs = []() {
+        std::vector<float> costs;
+        if (const char* env = std::getenv("GGML_BATCH_COSTS")) {
+            for (const char* p = env; *p; ) {
+                char* end;
+                costs.push_back(std::strtof(p, &end));
+                p = *end == ',' ? end + 1 : end;
+            }
+        }
+        return costs;
+    }();
+    GGML_ASSERT(batch_costs.size() >= 2 && "GGML_BATCH_COSTS must have at least 2 values");
+
+    // read in from an environment variable for now (default = 0)
+    const size_t max_look_ahead = std::getenv("GGML_MAX_LOOK_AHEAD") ? atoi(getenv("GGML_MAX_LOOK_AHEAD")) : 0;
+
+    // the current sequence probability, as predicted by the draft
+    float sequence_p = 1.0;
+
+    // the longest draft size we have seen that is +EV
+    size_t best_size = 0;
+
     // sample n_draft tokens from the draft model
     for (int i = 0; i < params.n_draft; ++i) {
         common_batch_clear(batch);
@@ -335,8 +358,11 @@ llama_tokens common_speculative_gen_draft(
             break;
         }
 
-        // only collect very high-confidence draft tokens
-        if (cur_p->data[0].p < params.p_min) {
+        // only collect +EV draft tokens
+        sequence_p *= cur_p->data[0].p;
+        if (sequence_p > batch_costs[std::min(result.size(), batch_costs.size() - 1)]) {
+            best_size = result.size();
+        } else if (sequence_p <= batch_costs[std::min(result.size() + max_look_ahead, batch_costs.size() - 1)]) {
             break;
         }
 
@@ -348,6 +374,9 @@ llama_tokens common_speculative_gen_draft(
         prompt_dft.push_back(id);
     }
 
+    // truncate to the best we saw that was +EV
+    result.resize(best_size);
+
     if (!spec->vocab_dft_compatible) {
         std::string detokenized = common_detokenize(ctx_dft, result, true);
         detokenized = replace_to_tgt(spec, detokenized);