diff --git a/fuzz/fuzz_targets/differential.rs b/fuzz/fuzz_targets/differential.rs
index b72af67..c10311e 100644
--- a/fuzz/fuzz_targets/differential.rs
+++ b/fuzz/fuzz_targets/differential.rs
@@ -38,7 +38,7 @@ fuzz_target!(
         let mut parsed_module =
             Module::from_wasm_bytes(&orig_bytes[..], &FrontendOptions::default()).unwrap();
         parsed_module.expand_all_funcs().unwrap();
-        parsed_module.per_func_body(|body| body.optimize());
+        parsed_module.per_func_body(|body| body.optimize(&mut waffle::passes::Fuel::infinite()));
         let roundtrip_bytes = parsed_module.to_wasm_bytes().unwrap();
 
         if let Ok(filename) = std::env::var("FUZZ_DUMP_WASM") {
diff --git a/src/backend/localify.rs b/src/backend/localify.rs
index 20b4596..f6e8c4e 100644
--- a/src/backend/localify.rs
+++ b/src/backend/localify.rs
@@ -6,7 +6,8 @@ use crate::cfg::CFGInfo;
 use crate::entity::{EntityVec, PerEntity};
 use crate::ir::{Block, FunctionBody, Local, Type, Value, ValueDef};
 use smallvec::{smallvec, SmallVec};
-use std::collections::{hash_map::Entry, HashMap};
+use std::collections::{HashMap, HashSet};
+use std::ops::Range;
 
 #[derive(Clone, Debug, Default)]
 pub struct Localifier {
@@ -26,14 +27,89 @@ struct Context<'a> {
     trees: &'a Trees,
     results: Localifier,
 
+    /// Precise liveness for each block: live Values at the end.
+    block_end_live: PerEntity<Block, HashSet<Value>>,
+
     /// Liveranges for each Value, in an arbitrary index space
     /// (concretely, the span of first to last instruction visit step
     /// index in an RPO walk over the function body).
-    ranges: HashMap<Value, std::ops::Range<usize>>,
+    ranges: HashMap<Value, Range<usize>>,
     /// Number of points.
     points: usize,
 }
 
+trait Visitor {
+    fn visit_use(&mut self, _: Value) {}
+    fn visit_def(&mut self, _: Value) {}
+    fn post_inst(&mut self, _: Value) {}
+    fn pre_inst(&mut self, _: Value) {}
+    fn post_term(&mut self) {}
+    fn pre_term(&mut self) {}
+    fn post_params(&mut self) {}
+    fn pre_params(&mut self) {}
+}
+
+struct BlockVisitor<'a, V: Visitor> {
+    body: &'a FunctionBody,
+    trees: &'a Trees,
+    visitor: V,
+}
+impl<'a, V: Visitor> BlockVisitor<'a, V> {
+    fn new(body: &'a FunctionBody, trees: &'a Trees, visitor: V) -> Self {
+        Self {
+            body,
+            trees,
+            visitor,
+        }
+    }
+    fn visit_block(&mut self, block: Block) {
+        self.visitor.post_term();
+        self.body.blocks[block].terminator.visit_uses(|u| {
+            self.visit_use(u);
+        });
+        self.visitor.pre_term();
+
+        for &inst in self.body.blocks[block].insts.iter().rev() {
+            self.visitor.post_inst(inst);
+            self.visit_inst(inst, /* root = */ true);
+            self.visitor.pre_inst(inst);
+        }
+
+        self.visitor.post_params();
+        for &(_, param) in &self.body.blocks[block].params {
+            self.visitor.visit_def(param);
+        }
+        self.visitor.pre_params();
+    }
+    fn visit_inst(&mut self, value: Value, root: bool) {
+        // If this is an instruction...
+        if let ValueDef::Operator(_, ref args, _) = &self.body.values[value] {
+            // If root, we need to process the def.
+            if root {
+                self.visitor.visit_def(value);
+            }
+            // Handle uses.
+            for &arg in args {
+                self.visit_use(arg);
+            }
+        }
+        // Otherwise, it may be an alias (but resolved above) or
+        // PickOutput, which we "see through" in handle_use of
+        // consumers.
+    }
+    fn visit_use(&mut self, value: Value) {
+        let value = self.body.resolve_alias(value);
+        if self.trees.owner.contains_key(&value) {
+            // If this is a treeified value, then don't process the use,
+            // but process the instruction directly here.
+            self.visit_inst(value, /* root = */ false);
+        } else {
+            // Otherwise, this is a proper use.
+            self.visitor.visit_use(value);
+        }
+    }
+}
+
 impl<'a> Context<'a> {
     fn new(body: &'a FunctionBody, cfg: &'a CFGInfo, trees: &'a Trees) -> Self {
         let mut results = Localifier::default();
@@ -49,122 +125,106 @@ impl<'a> Context<'a> {
             cfg,
             trees,
             results,
+            block_end_live: PerEntity::default(),
             ranges: HashMap::default(),
             points: 0,
         }
     }
 
+    fn compute_liveness(&mut self) {
+        struct LivenessVisitor {
+            live: HashSet<Value>,
+        }
+        impl Visitor for LivenessVisitor {
+            fn visit_use(&mut self, value: Value) {
+                self.live.insert(value);
+            }
+            fn visit_def(&mut self, value: Value) {
+                self.live.remove(&value);
+            }
+        }
+
+        let mut workqueue: Vec<Block> = self.cfg.rpo.values().cloned().collect();
+        let mut workqueue_set: HashSet<Block> = workqueue.iter().cloned().collect();
+        while let Some(block) = workqueue.pop() {
+            let live = self.block_end_live[block].clone();
+            let mut visitor = BlockVisitor::new(self.body, self.trees, LivenessVisitor { live });
+            visitor.visit_block(block);
+            let live = visitor.visitor.live;
+
+            for &pred in &self.body.blocks[block].preds {
+                let pred_live = &mut self.block_end_live[pred];
+                let mut changed = false;
+                for &value in &live {
+                    if pred_live.insert(value) {
+                        changed = true;
+                    }
+                }
+                if changed && workqueue_set.insert(pred) {
+                    workqueue.push(pred);
+                }
+            }
+        }
+    }
+
     fn find_ranges(&mut self) {
         let mut point = 0;
 
-        let mut live: HashMap<Value, usize> = HashMap::default();
-        let mut block_starts: HashMap<Block, usize> = HashMap::default();
+        struct LiveRangeVisitor<'b> {
+            point: &'b mut usize,
+            live: HashMap<Value, usize>,
+            ranges: &'b mut HashMap<Value, Range<usize>>,
+        }
+        impl<'b> Visitor for LiveRangeVisitor<'b> {
+            fn pre_params(&mut self) {
+                *self.point += 1;
+            }
+            fn pre_inst(&mut self, _: Value) {
+                *self.point += 1;
+            }
+            fn pre_term(&mut self) {
+                *self.point += 1;
+            }
+            fn visit_use(&mut self, value: Value) {
+                self.live.entry(value).or_insert(*self.point);
+            }
+            fn visit_def(&mut self, value: Value) {
+                let range = if let Some(start) = self.live.remove(&value) {
+                    start..(*self.point + 1)
+                } else {
+                    *self.point..(*self.point + 1)
+                };
+                let existing_range = self.ranges.entry(value).or_insert(range.clone());
+                existing_range.start = std::cmp::min(existing_range.start, range.start);
+                existing_range.end = std::cmp::max(existing_range.end, range.end);
+            }
+        }
+
         for &block in self.cfg.rpo.values().rev() {
-            block_starts.insert(block, point);
-
-            self.body.blocks[block].terminator.visit_uses(|u| {
-                self.handle_use(&mut live, &mut point, u);
-            });
-            point += 1;
-
-            for &inst in self.body.blocks[block].insts.iter().rev() {
-                self.handle_inst(&mut live, &mut point, inst, /* root = */ true);
-                point += 1;
+            let visitor = LiveRangeVisitor {
+                live: HashMap::default(),
+                point: &mut point,
+                ranges: &mut self.ranges,
+            };
+            let mut visitor = BlockVisitor::new(&self.body, &self.trees, visitor);
+            // Live-outs to succ blocks: in this block-local
+            // handling, model them as uses as the end of the block.
+            for &livein in &self.block_end_live[block] {
+                visitor.visitor.visit_use(livein);
             }
-
-            for &(_, param) in &self.body.blocks[block].params {
-                self.handle_def(&mut live, &mut point, param);
-            }
-            point += 1;
-
-            // If there were any in-edges from blocks numbered earlier
-            // in postorder ("loop backedges"), extend the start of
-            // the backward-range on all live values at this point to
-            // the origin of the edge. (In forward program order,
-            // extend the *end* of the liverange down to the end of
-            // the loop.)
-            //
-            // Note that we do this *after* inserting our own start
-            // above, so we handle self-loops properly.
-            for &pred in &self.body.blocks[block].preds {
-                if let Some(&start) = block_starts.get(&pred) {
-                    for live_start in live.values_mut() {
-                        *live_start = std::cmp::min(*live_start, start);
-                    }
-                }
+            // Visit all insts.
+            visitor.visit_block(block);
+            // Live-ins from pred blocks: anything still live has a
+            // virtual def at top of block.
+            let still_live = visitor.visitor.live.keys().cloned().collect::<Vec<_>>();
+            for live in still_live {
+                visitor.visitor.visit_def(live);
             }
         }
 
         self.points = point;
     }
 
-    fn handle_def(&mut self, live: &mut HashMap<Value, usize>, point: &mut usize, value: Value) {
-        // If the value was not live, make it so just for this
-        // point. Otherwise, end the liverange.
-        log::trace!("localify: point {}: live {:?}: def {}", point, live, value);
-        match live.entry(value) {
-            Entry::Vacant(_) => {
-                log::trace!(" -> was dead; use {}..{}", *point, *point + 1);
-                self.ranges.insert(value, *point..(*point + 1));
-            }
-            Entry::Occupied(o) => {
-                let start = o.remove();
-                log::trace!(" -> was live; use {}..{}", start, *point + 1);
-                self.ranges.insert(value, start..(*point + 1));
-            }
-        }
-    }
-
-    fn handle_use(&mut self, live: &mut HashMap<Value, usize>, point: &mut usize, value: Value) {
-        let value = self.body.resolve_alias(value);
-        log::trace!("localify: point {}: live {:?}: use {}", point, live, value);
-        if self.trees.owner.contains_key(&value) {
-            log::trace!(" -> treeified, going to inst");
-            // If this is a treeified value, then don't process the use,
-            // but process the instruction directly here.
-            self.handle_inst(live, point, value, /* root = */ false);
-        } else {
-            // Otherwise, update liveranges: make value live at this
-            // point if not live already.
-            live.entry(value).or_insert(*point);
-        }
-    }
-
-    fn handle_inst(
-        &mut self,
-        live: &mut HashMap<Value, usize>,
-        point: &mut usize,
-        value: Value,
-        root: bool,
-    ) {
-        log::trace!(
-            "localify: point {}: live {:?}: handling inst {} root {}",
-            point,
-            live,
-            value,
-            root
-        );
-
-        // If this is an instruction...
-        if let ValueDef::Operator(_, ref args, _) = &self.body.values[value] {
-            // If root, we need to process the def.
-            if root {
-                *point += 1;
-                log::trace!(" -> def {}", value);
-                self.handle_def(live, point, value);
-            }
-            *point += 1;
-            // Handle uses.
-            for &arg in args {
-                log::trace!(" -> arg {}", arg);
-                self.handle_use(live, point, arg);
-            }
-        }
-        // Otherwise, it may be an alias (but resolved above) or
-        // PickOutput, which we "see through" in handle_use of
-        // consumers.
-    }
-
     fn allocate(&mut self) {
         // Sort values by ranges' starting points, then value to break ties.
         let mut ranges: Vec<(Value, std::ops::Range<usize>)> =
@@ -181,16 +241,6 @@ impl<'a> Context<'a> {
         let mut freelist: HashMap<Type, Vec<Local>> = HashMap::new();
 
         for i in 0..self.points {
-            // Process ends. (Ends are exclusive, so we do them
-            // first; another range can grab the local at the same
-            // point index in this same iteration.)
-            if let Some(expiring) = expiring.remove(&i) {
-                for (ty, local) in expiring {
-                    log::trace!(" -> expiring {} of type {} back to freelist", local, ty);
-                    freelist.entry(ty).or_insert_with(|| vec![]).push(local);
-                }
-            }
-
             // Process starts.
             while range_idx < ranges.len() && ranges[range_idx].1.start == i {
                 let (value, range) = ranges[range_idx].clone();
@@ -228,10 +278,21 @@ impl<'a> Context<'a> {
                 }
                 self.results.values[value] = allocs;
             }
+
+            // Process ends. (Ends are exclusive, so we do them
+            // first; another range can grab the local at the same
+            // point index in this same iteration.)
+            if let Some(expiring) = expiring.remove(&i) {
+                for (ty, local) in expiring {
+                    log::trace!(" -> expiring {} of type {} back to freelist", local, ty);
+                    freelist.entry(ty).or_insert_with(|| vec![]).push(local);
+                }
+            }
         }
     }
 
     fn compute(mut self) -> Localifier {
+        self.compute_liveness();
         self.find_ranges();
         self.allocate();
         self.results
diff --git a/src/bin/waffle-util.rs b/src/bin/waffle-util.rs
index 5f1c7e3..fd142a4 100644
--- a/src/bin/waffle-util.rs
+++ b/src/bin/waffle-util.rs
@@ -57,7 +57,7 @@ enum Command {
 fn apply_options(opts: &Options, module: &mut Module) -> Result<()> {
     module.expand_all_funcs()?;
     if opts.basic_opts {
-        module.per_func_body(|body| body.optimize());
+        module.per_func_body(|body| body.optimize(&mut waffle::passes::Fuel::infinite()));
     }
     if opts.max_ssa {
         module.per_func_body(|body| body.convert_to_max_ssa());
diff --git a/src/passes.rs b/src/passes.rs
index 11dc04c..c5e47fe 100644
--- a/src/passes.rs
+++ b/src/passes.rs
@@ -14,6 +14,9 @@ pub struct Fuel {
 }
 impl Fuel {
     pub fn consume(&mut self) -> bool {
+        if self.remaining == u64::MAX {
+            return true;
+        }
         if self.remaining == 0 {
             false
         } else {
@@ -21,4 +24,9 @@ impl Fuel {
             true
         }
     }
+    pub fn infinite() -> Fuel {
+        Fuel {
+            remaining: u64::MAX,
+        }
+    }
 }
diff --git a/src/passes/basic_opt.rs b/src/passes/basic_opt.rs
index 828fb0f..971bfb7 100644
--- a/src/passes/basic_opt.rs
+++ b/src/passes/basic_opt.rs
@@ -47,10 +47,6 @@ impl<'a> GVNPass<'a> {
     fn optimize(&mut self, block: Block, body: &mut FunctionBody) {
         let mut i = 0;
         while i < body.blocks[block].insts.len() {
-            if !self.fuel.consume() {
-                return;
-            }
-
             let inst = body.blocks[block].insts[i];
             i += 1;
             if value_is_pure(inst, body) {
@@ -115,6 +111,10 @@ impl<'a> GVNPass<'a> {
                 }
 
                 if let Some(value) = self.map.get(&value) {
+                    if !self.fuel.consume() {
+                        return;
+                    }
+
                     body.set_alias(inst, *value);
                     i -= 1;
                     body.blocks[block].insts.remove(i);