diff --git a/csrc/kernels/attn_dispatchers.cuh b/csrc/kernels/attn_dispatchers.cuh
index 52d2a8d..658935e 100644
--- a/csrc/kernels/attn_dispatchers.cuh
+++ b/csrc/kernels/attn_dispatchers.cuh
@@ -15,11 +15,15 @@
 #endif
 
 // Split-KV: compute number of splits to fill all SMs for small-batch decode.
-inline int compute_num_splits(int base_blocks, int tiles_total) {
+// Caps splits so each split processes at least `min_tiles_per_split` tiles,
+// avoiding excessive loop/prologue overhead when tiles are small.
+inline int compute_num_splits(int base_blocks, int tiles_total,
+                              int min_tiles_per_split = 1) {
     int sm_count = 0;
     cudaDeviceGetAttribute(&sm_count, cudaDevAttrMultiProcessorCount, 0);
     int n = (2 * sm_count + base_blocks - 1) / base_blocks;
-    return std::max(1, std::min(n, std::min(tiles_total, MAX_SPLITS)));
+    int max_by_work = tiles_total / min_tiles_per_split;
+    return std::max(1, std::min(n, std::min(max_by_work, MAX_SPLITS)));
 }
 
 // ======================================================================
@@ -75,15 +79,20 @@ static inline void dispatch_prefill(AttentionParams<bf16>& p) {
 // ======================================================================
 
 #ifndef ASTRAI_NO_MMA
+// BC=16: halves smem (16KB vs 32KB) → doubles occupancy (6 vs 3 blocks/SM).
+// For D=256, BC=16 also reduces register pressure (fewer Sacc/PV frags),
+// enabling STAGES=2 (double-buffer) within the 32KB smem budget — eliminates
+// the 176-byte spill that STAGES=1+BC=32 suffered.
 template <int HEAD_DIM, bool IsCausal, bool HasMask>
 static inline void launch_decode_mma(AttentionParams<bf16>& p, int group_size) {
     int G = p.q_head / p.kv_head;
     constexpr int MAX_G = 16;
     int num_passes = (G + MAX_G - 1) / MAX_G;
-    int tiles_total = (p.kv_len + 32 - 1) / 32;
-    p.num_splits = compute_num_splits(p.batch * p.kv_head, tiles_total);
-    constexpr int STAGES = (HEAD_DIM <= 128) ? 2 : 1;
-    using Traits = KernelTraits<HEAD_DIM, 32, 1, STAGES>;
+    constexpr int BC = 16;
+    int tiles_total = (p.kv_len + BC - 1) / BC;
+    p.num_splits = compute_num_splits(p.batch * p.kv_head, tiles_total, 2);
+    constexpr int STAGES = 2;
+    using Traits = KernelTraits<HEAD_DIM, BC, 1, STAGES>;
     dim3 grid(p.kv_head * num_passes, p.batch, p.num_splits);
     attn_decode_split_kv_mma_kernel<Traits, IsCausal, HasMask><<<grid, 32>>>(p);
 }
@@ -136,13 +145,16 @@ template <int HEAD_DIM, bool IsCausal, bool HasMask>
 static inline void launch_paged_decode_mma(PagedAttentionParams<bf16>& p, int group_size) {
     int G = p.q_head / p.kv_head;
     constexpr int MAX_G = 16;
-    bool page_ok = (p.page_size >= 32);
+    constexpr int BC = 16;
+    // page_size must be >= BC and a multiple of BC so a BC-wide tile never
+    // straddles two pages (the kernel does one page-table lookup per tile).
+    bool page_ok = (p.page_size >= BC) && (p.page_size % BC == 0);
     if (G >= 1 && page_ok) {
         int num_passes = (G + MAX_G - 1) / MAX_G;
-        int tiles_total = (p.kv_len + 32 - 1) / 32;
-        p.num_splits = compute_num_splits(p.batch * p.kv_head, tiles_total);
-        constexpr int STAGES = (HEAD_DIM <= 128) ? 2 : 1;
-        using Traits = KernelTraits<HEAD_DIM, 32, 1, STAGES>;
+        int tiles_total = (p.kv_len + BC - 1) / BC;
+        p.num_splits = compute_num_splits(p.batch * p.kv_head, tiles_total, 2);
+        constexpr int STAGES = 2;
+        using Traits = KernelTraits<HEAD_DIM, BC, 1, STAGES>;
         dim3 grid(p.kv_head * num_passes, p.batch, p.num_splits);
         paged_attn_decode_split_kv_mma_kernel<Traits, IsCausal, HasMask> <<<grid, 32>>>(p);
     } else {