diff --git a/src/nouveau/compiler/nak/api.rs b/src/nouveau/compiler/nak/api.rs
index 1cfb01b64b5..6e25244912b 100644
--- a/src/nouveau/compiler/nak/api.rs
+++ b/src/nouveau/compiler/nak/api.rs
@@ -200,6 +200,7 @@ pub extern "C" fn nak_compiler_create(
     let nak = Box::new(nak_compiler {
         sm: dev.sm,
         warps_per_sm: dev.max_warps_per_mp,
+        blocks_per_sm: dev.max_blocks_per_mp,
         max_shared_mem: u32::from(
             dev.sm_smem_sizes_kB[usize::from(dev.sm_smem_size_count) - 1],
         ) * 1024,
@@ -452,7 +453,12 @@ fn nak_compile_shader_internal(
         Some(unsafe { &*fs_key })
     };
 
-    let sm = ShaderModelInfo::new(nak.sm, nak.warps_per_sm, nak.max_shared_mem);
+    let sm = ShaderModelInfo::new(
+        nak.sm,
+        nak.warps_per_sm,
+        nak.blocks_per_sm,
+        nak.max_shared_mem,
+    );
     let mut s = nak_shader_from_nir(nak, nir, &sm);
 
     if DEBUG.print() {
diff --git a/src/nouveau/compiler/nak/hw_tests.rs b/src/nouveau/compiler/nak/hw_tests.rs
index decaf6e00a9..a1c234389e1 100644
--- a/src/nouveau/compiler/nak/hw_tests.rs
+++ b/src/nouveau/compiler/nak/hw_tests.rs
@@ -37,8 +37,12 @@ impl RunSingleton {
 
             let run = Runner::new(dev_id);
             let sm_nr = run.dev_info().sm;
-            let sm =
-                ShaderModelInfo::new(sm_nr, run.dev_info().max_warps_per_mp, 0);
+            let sm = ShaderModelInfo::new(
+                sm_nr,
+                run.dev_info().max_warps_per_mp,
+                0,
+                0,
+            );
             RunSingleton { sm, run }
         })
     }
diff --git a/src/nouveau/compiler/nak/ir.rs b/src/nouveau/compiler/nak/ir.rs
index 3e90f6a38ee..80dff25e0df 100644
--- a/src/nouveau/compiler/nak/ir.rs
+++ b/src/nouveau/compiler/nak/ir.rs
@@ -9774,14 +9774,21 @@ pub trait ShaderModel {
 pub struct ShaderModelInfo {
     sm: u8,
     warps_per_sm: u8,
+    blocks_per_sm: u8,
     shared_mem_per_sm: u32,
 }
 
 impl ShaderModelInfo {
-    pub fn new(sm: u8, warps_per_sm: u8, shared_mem_per_sm: u32) -> Self {
+    pub fn new(
+        sm: u8,
+        warps_per_sm: u8,
+        blocks_per_sm: u8,
+        shared_mem_per_sm: u32,
+    ) -> Self {
         ShaderModelInfo {
             sm,
             warps_per_sm,
+            blocks_per_sm,
             shared_mem_per_sm,
         }
     }
@@ -9910,7 +9917,6 @@ pub fn max_warps_per_sm(
     shared_mem: u16,
     block_size: u16,
 ) -> u32 {
-    // TODO: Take local_size and max blocks/SM into account for compute
     let total_regs: u32 = 65536;
     // GPRs are allocated in multiples of 8
     let gprs = max(gprs, 1);
@@ -9918,6 +9924,12 @@ pub fn max_warps_per_sm(
     let mut max_warps = prev_multiple_of((total_regs / 32) / gprs, 4);
     let block_size = u32::from(block_size.next_multiple_of(32));
 
+    // Next we limit the warps according to our available blocks
+    if block_size != 0 {
+        max_warps =
+            max_warps.min((block_size * u32::from(sm.blocks_per_sm)) / 32);
+    }
+
     // Next we limit the warps according to our available shared memory
     if shared_mem != 0 && block_size != 0 {
         let max_blocks = sm.shared_mem_per_sm / u32::from(shared_mem);
diff --git a/src/nouveau/compiler/nak/nvdisasm_tests.rs b/src/nouveau/compiler/nak/nvdisasm_tests.rs
index 5d097816172..1281e50ad7d 100644
--- a/src/nouveau/compiler/nak/nvdisasm_tests.rs
+++ b/src/nouveau/compiler/nak/nvdisasm_tests.rs
@@ -87,7 +87,7 @@ fn disassemble_instrs(instrs: Vec<Instr>, sm: u8) -> Vec<String> {
         io: ShaderIoInfo::None,
     };
 
-    let sm = ShaderModelInfo::new(sm, 0, 0);
+    let sm = ShaderModelInfo::new(sm, 0, 0, 0);
     let s = Shader {
         sm: &sm,
         info: info,
diff --git a/src/nouveau/compiler/nak/opt_instr_sched_prepass.rs b/src/nouveau/compiler/nak/opt_instr_sched_prepass.rs
index 955f290518d..3893a3fcf93 100644
--- a/src/nouveau/compiler/nak/opt_instr_sched_prepass.rs
+++ b/src/nouveau/compiler/nak/opt_instr_sched_prepass.rs
@@ -42,7 +42,7 @@ fn next_occupancy_cliff(sm: &ShaderModelInfo, x: u32) -> u32 {
 #[test]
 fn test_next_occupancy_cliff() {
     for max_hw_warps in [32, 48, 64] {
-        let sm = ShaderModelInfo::new(75, max_hw_warps, 100 * 1024);
+        let sm = ShaderModelInfo::new(75, max_hw_warps, 0, 100 * 1024);
         for x in 0..255 {
             let y = next_occupancy_cliff(&sm, x);
             assert!(y >= x);
diff --git a/src/nouveau/compiler/nak_private.h b/src/nouveau/compiler/nak_private.h
index 18eaab11f33..29930f4f2f3 100644
--- a/src/nouveau/compiler/nak_private.h
+++ b/src/nouveau/compiler/nak_private.h
@@ -20,6 +20,7 @@ bool nak_debug_no_ugpr(void);
 struct nak_compiler {
    uint8_t sm;
    uint8_t warps_per_sm;
+   uint8_t blocks_per_sm;
    uint32_t max_shared_mem;
 
    struct nir_shader_compiler_options nir_options;