diff --git a/fuzz/fuzz_targets/opt_diff.rs b/fuzz/fuzz_targets/opt_diff.rs
index d910e17..6610053 100644
--- a/fuzz/fuzz_targets/opt_diff.rs
+++ b/fuzz/fuzz_targets/opt_diff.rs
@@ -49,7 +49,7 @@ fuzz_target!(
 
         let mut opt_module = parsed_module.clone();
         opt_module.per_func_body(|body| body.optimize());
-        opt_module.per_func_body(|body| body.convert_to_max_ssa());
+        opt_module.per_func_body(|body| body.convert_to_max_ssa(None));
 
         let mut opt_ctx = InterpContext::new(&opt_module).unwrap();
         // Allow a little leeway for opts to not actually optimize.
diff --git a/src/bin/waffle-util.rs b/src/bin/waffle-util.rs
index 2f13230..ae52cf3 100644
--- a/src/bin/waffle-util.rs
+++ b/src/bin/waffle-util.rs
@@ -67,7 +67,7 @@ fn apply_options(opts: &Options, module: &mut Module) -> Result<()> {
         module.per_func_body(|body| body.optimize());
     }
     if opts.max_ssa {
-        module.per_func_body(|body| body.convert_to_max_ssa());
+        module.per_func_body(|body| body.convert_to_max_ssa(None));
     }
     Ok(())
 }
diff --git a/src/ir/func.rs b/src/ir/func.rs
index d4694ff..a06c2a4 100644
--- a/src/ir/func.rs
+++ b/src/ir/func.rs
@@ -4,6 +4,7 @@ use crate::entity::{EntityRef, EntityVec, PerEntity};
 use crate::frontend::parse_body;
 use crate::ir::SourceLoc;
 use anyhow::Result;
+use std::collections::HashSet;
 
 /// A declaration of a function: there is one `FuncDecl` per `Func`
 /// index.
@@ -50,10 +51,10 @@ impl<'a> FuncDecl<'a> {
         }
     }
 
-    pub fn convert_to_max_ssa(&mut self) {
+    pub fn convert_to_max_ssa(&mut self, cut_blocks: Option<HashSet<Block>>) {
         match self {
             FuncDecl::Body(_, _, body) => {
-                body.convert_to_max_ssa();
+                body.convert_to_max_ssa(cut_blocks);
             }
             _ => {}
         }
@@ -150,9 +151,9 @@ impl FunctionBody {
         crate::passes::empty_blocks::run(self);
     }
 
-    pub fn convert_to_max_ssa(&mut self) {
+    pub fn convert_to_max_ssa(&mut self, cut_blocks: Option<HashSet<Block>>) {
         let cfg = crate::cfg::CFGInfo::new(self);
-        crate::passes::maxssa::run(self, &cfg);
+        crate::passes::maxssa::run(self, cut_blocks, &cfg);
     }
 
     pub fn add_block(&mut self) -> Block {
diff --git a/src/passes/maxssa.rs b/src/passes/maxssa.rs
index 4987470..bed6caf 100644
--- a/src/passes/maxssa.rs
+++ b/src/passes/maxssa.rs
@@ -7,13 +7,16 @@
 use crate::cfg::CFGInfo;
 use crate::entity::PerEntity;
 use crate::ir::{Block, FunctionBody, Value, ValueDef};
-use std::collections::{BTreeSet, HashMap};
+use std::collections::{BTreeSet, HashMap, HashSet};
 
-pub fn run(body: &mut FunctionBody, cfg: &CFGInfo) {
-    MaxSSAPass::new().run(body, cfg);
+pub fn run(body: &mut FunctionBody, cut_blocks: Option<HashSet<Block>>, cfg: &CFGInfo) {
+    MaxSSAPass::new(cut_blocks).run(body, cfg);
 }
 
 struct MaxSSAPass {
+    /// Blocks at which all live values must cross through blockparams
+    /// (or if None, then all blocks).
+    cut_blocks: Option<HashSet<Block>>,
     /// Additional block args that must be passed to each block, in
     /// order. Value numbers are *original* values.
     new_args: PerEntity<Block, Vec<Value>>,
@@ -23,8 +26,9 @@ struct MaxSSAPass {
 }
 
 impl MaxSSAPass {
-    fn new() -> Self {
+    fn new(cut_blocks: Option<HashSet<Block>>) -> Self {
         Self {
+            cut_blocks,
             new_args: PerEntity::default(),
             value_map: HashMap::new(),
         }
@@ -76,7 +80,7 @@ impl MaxSSAPass {
         }
         self.new_args[block].push(value);
 
-        // Create a blockparam.
+        // Create a placeholder value.
         let ty = body.values[value].ty().unwrap();
         let blockparam = body.add_blockparam(block, ty);
         self.value_map.insert((block, value), blockparam);
@@ -89,24 +93,44 @@ impl MaxSSAPass {
             let pred = body.blocks[block].preds[i];
             self.visit_use(body, cfg, pred, value);
         }
+
+        // If all preds have the same value, and this is not a
+        // cut-block, rewrite the blockparam to an alias instead.
+        if !self.is_cut_block(block) {
+            if let Some(pred_value) = iter_all_same(
+                body.blocks[block]
+                    .preds
+                    .iter()
+                    .map(|&pred| *self.value_map.get(&(pred, value)).unwrap_or(&value))
+                    .filter(|&val| val != blockparam),
+            ) {
+                body.blocks[block].params.pop();
+                self.new_args[block].pop();
+                body.values[blockparam] = ValueDef::Alias(pred_value);
+                self.value_map.insert((block, value), pred_value);
+            }
+        }
     }
 
-    fn update_preds(&mut self, body: &mut FunctionBody, block: Block) {
-        for i in 0..body.blocks[block].preds.len() {
-            let pred = body.blocks[block].preds[i];
-            let pred_succ_idx = body.blocks[block].pos_in_pred_succ[i];
-            body.blocks[pred]
-                .terminator
-                .update_target(pred_succ_idx, |target| {
-                    for &new_arg in &self.new_args[block] {
-                        let actual_value = self
-                            .value_map
-                            .get(&(pred, new_arg))
-                            .copied()
-                            .unwrap_or(new_arg);
-                        target.args.push(actual_value);
-                    }
-                });
+    fn is_cut_block(&self, block: Block) -> bool {
+        self.cut_blocks
+            .as_ref()
+            .map(|cut_blocks| cut_blocks.contains(&block))
+            .unwrap_or(true)
+    }
+
+    fn update_branch_args(&mut self, body: &mut FunctionBody) {
+        for (block, blockdata) in body.blocks.entries_mut() {
+            blockdata.terminator.update_targets(|target| {
+                for &new_arg in &self.new_args[target.block] {
+                    let actual_value = self
+                        .value_map
+                        .get(&(block, new_arg))
+                        .copied()
+                        .unwrap_or(new_arg);
+                    target.args.push(actual_value);
+                }
+            });
         }
     }
 
@@ -147,11 +171,19 @@ impl MaxSSAPass {
     }
 
     fn update(&mut self, body: &mut FunctionBody) {
+        self.update_branch_args(body);
         for block in body.blocks.iter() {
-            if self.new_args[block].len() > 0 {
-                self.update_preds(body, block);
-            }
             self.update_uses(body, block);
         }
     }
 }
+
+fn iter_all_same<Item: PartialEq + Eq + Copy, I: Iterator<Item = Item>>(iter: I) -> Option<Item> {
+    let mut item = None;
+    for val in iter {
+        if *item.get_or_insert(val) != val {
+            return None;
+        }
+    }
+    item
+}