diff --git a/Makefile b/Makefile
index 2167a9d..e37d3d5 100644
--- a/Makefile
+++ b/Makefile
@@ -75,6 +75,16 @@ else
   ifneq ($(shell $(CXX) -fopenmp -E - < /dev/null 2>/dev/null && echo yes),)
     LDFLAGS += -lgomp
   endif
+  # ggml-cuda.a leaves the CUDA runtime, cuBLAS, and driver API unresolved.
+  # The stubs dir lets -lcuda link on hosts without a driver (e.g. release CI);
+  # the real libcuda.so.1 is picked up from the driver at load time.
+  ifneq (,$(filter -DGGML_CUDA=ON,$(CMAKE_FLAGS)))
+    CUDA_HOME ?= $(patsubst %/bin/nvcc,%,$(shell which nvcc 2>/dev/null))
+    ifneq ($(CUDA_HOME),)
+      LDFLAGS += -L$(CUDA_HOME)/lib64 -L$(CUDA_HOME)/lib64/stubs
+    endif
+    LDFLAGS += -lcudart -lcublas -lcublasLt -lcuda
+  endif
 endif
 
 # CPU count for parallel builds
diff --git a/c_src/llama_cpp_ex/llama_nif.cpp b/c_src/llama_cpp_ex/llama_nif.cpp
index 31ffd67..35716c6 100644
--- a/c_src/llama_cpp_ex/llama_nif.cpp
+++ b/c_src/llama_cpp_ex/llama_nif.cpp
@@ -1794,11 +1794,19 @@ fine::Ok<> generate_mtp_tokens(
 
                 // Re-decode the accepted tokens on the target so the next
                 // iteration's draft starts from a consistent state.
+                //
+                // The KV must be rebuilt with the token that was `sampled` at
+                // the top of this iteration (batch element 0, at pos n_past),
+                // followed by all but the LAST emitted token. The last emitted
+                // token becomes the next iteration's `sampled` and is decoded
+                // then — including it here would duplicate it in the context.
+                // `sampled` sits at prompt[size - n_accepted_total - 1], since
+                // the accept loop pushed n_accepted_total tokens after it.
                 if (n_accepted_total > 0) {
                     llama_batch redo = llama_batch_init(n_accepted_total, 0, 1);
                     for (int i = 0; i < n_accepted_total; i++) {
                         llama_token tok =
-                            prompt[prompt.size() - n_accepted_total + i];
+                            prompt[prompt.size() - n_accepted_total - 1 + i];
                         common_batch_add(redo, tok,
                                          n_past + static_cast<llama_pos>(i),
                                          { seq_id },