diff --git a/compiler/optimizer/demand.go b/compiler/optimizer/demand.go
index 6e9057ed04..f6f68f6b50 100644
--- a/compiler/optimizer/demand.go
+++ b/compiler/optimizer/demand.go
@@ -5,132 +5,240 @@ import (
 	"github.com/brimdata/super/compiler/optimizer/demand"
 )
 
-func insertDemand(seq dag.Seq) dag.Seq {
-	demands := InferDemandSeqOut(seq)
-	return walk(seq, true, func(seq dag.Seq) dag.Seq {
-		for _, op := range seq {
-			switch op := op.(type) {
-			case *dag.FileScan:
-				op.Fields = demand.Fields(demands[op])
-			case *dag.SeqScan:
-				op.Fields = demand.Fields(demands[op])
-			}
-		}
-		return seq
-	})
-}
-
-// Returns a map from op to the demand on the output of that op.
-func InferDemandSeqOut(seq dag.Seq) map[dag.Op]demand.Demand {
-	demands := make(map[dag.Op]demand.Demand)
-	inferDemandSeqOutWith(demands, demand.All(), seq)
-	for _, d := range demands {
-		if !demand.IsValid(d) {
-			panic("Invalid demand")
-		}
+func DemandForSeq(seq dag.Seq, downstream demand.Demand) demand.Demand {
+	for i := len(seq) - 1; i >= 0; i-- {
+		downstream = demandForOp(seq[i], downstream)
 	}
-	return demands
+	return downstream
 }
 
-func inferDemandSeqOutWith(demands map[dag.Op]demand.Demand, demandSeqOut demand.Demand, seq dag.Seq) {
-	demandOpOut := demandSeqOut
-	for i := len(seq) - 1; i >= 0; i-- {
-		op := seq[i]
-		if _, ok := demands[op]; ok {
-			panic("Duplicate op value")
+func demandForOp(op dag.Op, downstream demand.Demand) demand.Demand {
+	switch op := op.(type) {
+	case *dag.Combine:
+		return downstream
+	case *dag.Cut:
+		return demandForAssignments(op.Args, demand.None())
+	case *dag.Drop:
+		return downstream
+	case *dag.Explode:
+		d := demand.None()
+		for _, a := range op.Args {
+			d = demand.Union(d, demandForExpr(a))
 		}
-		demands[op] = demandOpOut
-
-		// Infer the demand that `op` places on it's input.
-		var demandOpIn demand.Demand
-		switch op := op.(type) {
-		case *dag.FileScan:
-			demandOpIn = demand.Union(demandOpOut, inferDemandExprIn(demand.All(), op.Filter))
-			demands[op] = demandOpIn
-		case *dag.Filter:
-			demandOpIn = demand.Union(
-				// Everything that downstream operations need.
-				demandOpOut,
-				// Everything that affects the outcome of this filter.
-				inferDemandExprIn(demand.All(), op.Expr),
-			)
-		case *dag.SeqScan:
-			demandOpIn = demand.Union(demandOpOut, inferDemandExprIn(demand.All(), op.Filter))
-			demands[op] = demandOpIn
-		case *dag.Summarize:
-			demandOpIn = demand.None()
-			// TODO If LHS not in demandOut, we can ignore RHS
-			for _, assignment := range op.Keys {
-				demandOpIn = demand.Union(demandOpIn, inferDemandExprIn(demand.All(), assignment.RHS))
-			}
-			for _, assignment := range op.Aggs {
-				demandOpIn = demand.Union(demandOpIn, inferDemandExprIn(demand.All(), assignment.RHS))
-			}
-		case *dag.Yield:
-			demandOpIn = demand.None()
-			for _, expr := range op.Exprs {
-				demandOpIn = demand.Union(demandOpIn, inferDemandExprIn(demandOpOut, expr))
-			}
-		default:
-			// Conservatively assume that `op` uses it's entire input, regardless of output demand.
-			demandOpIn = demand.All()
+		return d
+	case *dag.Filter:
+		return demand.Union(downstream, demandForExpr(op.Expr))
+	case *dag.Fork:
+		d := demand.None()
+		for _, p := range op.Paths {
+			d = demand.Union(d, DemandForSeq(p, downstream))
 		}
-		demandOpOut = demandOpIn
-	}
-}
+		return d
+	case *dag.Fuse:
+		return demand.All()
+	case *dag.Head:
+		return downstream
+	case *dag.Join:
+		d := downstream
+		d = demand.Union(d, demandForExpr(op.LeftKey))
+		d = demand.Union(d, demandForExpr(op.RightKey))
+		return demandForAssignments(op.Args, d)
+	case *dag.Load:
+		return demand.All()
+	case *dag.Merge:
+		return demand.Union(downstream, demandForExpr(op.Expr))
+	case *dag.Mirror:
+		return demand.Union(DemandForSeq(op.Main, demand.All()),
+			DemandForSeq(op.Mirror, demand.All()))
+	case *dag.Output:
+		return demand.All()
+	case *dag.Over:
+		d := demand.None()
+		for _, def := range op.Defs {
+			d = demand.Union(d, demandForExpr(def.Expr))
+		}
+		for _, e := range op.Exprs {
+			d = demand.Union(d, demandForExpr(e))
+		}
+		return d
+	case *dag.Pass:
+		return downstream
+	case *dag.Put:
+		return demandForAssignments(op.Args, downstream)
+	case *dag.Rename:
+		return demandForAssignments(op.Args, downstream)
+	case *dag.Scatter:
+		d := demand.None()
+		for _, p := range op.Paths {
+			d = demand.Union(d, DemandForSeq(p, downstream))
+		}
+		return d
+	case *dag.Scope:
+		return DemandForSeq(op.Body, downstream)
+	case *dag.Shape, *dag.Sort:
+		return downstream
+	case *dag.Summarize:
+		d := demand.None()
+		for _, assignment := range op.Keys {
+			d = demand.Union(d, demandForExpr(assignment.RHS))
+		}
+		for _, assignment := range op.Aggs {
+			d = demand.Union(d, demandForExpr(assignment.RHS))
+		}
+		return d
+	case *dag.Switch:
+		d := demandForExpr(op.Expr)
+		for _, c := range op.Cases {
+			d = demand.Union(d, demandForExpr(c.Expr))
+			d = demand.Union(d, DemandForSeq(c.Path, downstream))
+		}
+		return d
+	case *dag.Tail, *dag.Top, *dag.Uniq:
+		return downstream
+	case *dag.Vectorize:
+		return DemandForSeq(op.Body, downstream)
+	case *dag.Yield:
+		d := demand.None()
+		for _, e := range op.Exprs {
+			d = demand.Union(d, demandForExpr(e))
+		}
+		return d
 
-func inferDemandExprIn(demandOut demand.Demand, expr dag.Expr) demand.Demand {
-	if demand.IsNone(demandOut) {
+	case *dag.CommitMetaScan, *dag.DefaultScan, *dag.Deleter, *dag.DeleteScan, *dag.LakeMetaScan:
 		return demand.None()
-	}
-	if expr == nil {
+	case *dag.FileScan:
+		d := demand.Union(downstream, demandForExpr(op.Filter))
+		op.Fields = demand.Fields(d)
+		return demand.None()
+	case *dag.HTTPScan, *dag.Lister, *dag.NullScan, *dag.PoolMetaScan, *dag.PoolScan:
+		return demand.None()
+	case *dag.RobotScan:
+		return demandForExpr(op.Expr)
+	case *dag.SeqScan:
+		d := demand.Union(downstream, demandForExpr(op.Filter))
+		d = demand.Union(d, demandForExpr(op.KeyPruner))
+		op.Fields = demand.Fields(d)
+		return demand.None()
+	case *dag.Slicer:
 		return demand.None()
 	}
-	var demandIn demand.Demand
+	panic(op)
+}
+
+func demandForExpr(expr dag.Expr) demand.Demand {
 	switch expr := expr.(type) {
+	case nil:
+		return demand.None()
 	case *dag.Agg:
-		// Since we don't know how the expr.Name will transform the inputs, we have to assume demand.All.
-		return demand.Union(
-			inferDemandExprIn(demand.All(), expr.Expr),
-			inferDemandExprIn(demand.All(), expr.Where),
-		)
+		return demand.Union(demandForExpr(expr.Expr), demandForExpr(expr.Where))
+	case *dag.ArrayExpr:
+		return demandForArrayOrSetExpr(expr.Elems)
 	case *dag.BinaryExpr:
-		// Since we don't know how the expr.Op will transform the inputs, we have to assume demand.All.
-		demandIn = demand.Union(
-			inferDemandExprIn(demand.All(), expr.LHS),
-			inferDemandExprIn(demand.All(), expr.RHS),
-		)
+		return demand.Union(demandForExpr(expr.LHS), demandForExpr(expr.RHS))
+	case *dag.Call:
+		d := demand.None()
+		if expr.Name == "every" {
+			d = demand.Key("ts", demand.All())
+		}
+		for _, a := range expr.Args {
+			d = demand.Union(d, demandForExpr(a))
+		}
+		return d
+	case *dag.Conditional:
+		return demand.Union(demandForExpr(expr.Cond),
+			demand.Union(demandForExpr(expr.Then), demandForExpr(expr.Else)))
 	case *dag.Dot:
-		demandIn = demand.Key(expr.RHS, inferDemandExprIn(demandOut, expr.LHS))
+		return demandForExpr(expr.LHS)
+	case *dag.Func:
+		// return demand.All()
+	case *dag.IndexExpr:
+		return demand.Union(demandForExpr(expr.Expr), demandForExpr(expr.Index))
+	case *dag.IsNullExpr:
+		return demandForExpr(expr.Expr)
 	case *dag.Literal:
-		demandIn = demand.None()
+		return demand.None()
+	case *dag.MapCall:
+		return demandForExpr(expr.Expr)
 	case *dag.MapExpr:
-		demandIn = demand.None()
-		for _, entry := range expr.Entries {
-			demandIn = demand.Union(demandIn, inferDemandExprIn(demand.All(), entry.Key))
-			demandIn = demand.Union(demandIn, inferDemandExprIn(demand.All(), entry.Value))
+		d := demand.None()
+		for _, e := range expr.Entries {
+			d = demand.Union(d, demandForExpr(e.Key))
+			d = demand.Union(d, demandForExpr(e.Value))
+		}
+		return d
+	case *dag.OverExpr:
+		d := demand.None()
+		for _, def := range expr.Defs {
+			d = demand.Union(d, demandForExpr(def.Expr))
+		}
+		for _, e := range expr.Exprs {
+			d = demand.Union(d, demandForExpr(e))
 		}
+		return d
 	case *dag.RecordExpr:
-		demandIn = demand.None()
-		for _, elem := range expr.Elems {
-			switch elem := elem.(type) {
+		d := demand.None()
+		for _, e := range expr.Elems {
+			switch e := e.(type) {
 			case *dag.Field:
-				demandValueOut := demand.GetKey(demandOut, elem.Name)
-				if !demand.IsNone(demandValueOut) {
-					demandIn = demand.Union(demandIn, inferDemandExprIn(demandValueOut, elem.Value))
-				}
+				d = demand.Union(d, demandForExpr(e.Value))
 			case *dag.Spread:
-				demandIn = demand.Union(demandIn, inferDemandExprIn(demand.All(), elem.Expr))
+				d = demand.Union(d, demandForExpr(e.Expr))
+			default:
+				panic(e)
 			}
 		}
+		return d
+	case *dag.RegexpMatch:
+		return demandForExpr(expr.Expr)
+	case *dag.RegexpSearch:
+		return demandForExpr(expr.Expr)
+	case *dag.Search:
+		return demandForExpr(expr.Expr)
+	case *dag.SetExpr:
+		return demandForArrayOrSetExpr(expr.Elems)
+	case *dag.SliceExpr:
+		return demand.Union(demandForExpr(expr.Expr),
+			demand.Union(demandForExpr(expr.From), demandForExpr(expr.To)))
 	case *dag.This:
-		demandIn = demandOut
+		d := demand.All()
 		for i := len(expr.Path) - 1; i >= 0; i-- {
-			demandIn = demand.Key(expr.Path[i], demandIn)
+			d = demand.Key(expr.Path[i], d)
+		}
+		return d
+	case *dag.UnaryExpr:
+		return demandForExpr(expr.Operand)
+	case *dag.Var:
+		return demand.None()
+	}
+	panic(expr)
+}
+
+func demandForArrayOrSetExpr(elems []dag.VectorElem) demand.Demand {
+	d := demand.None()
+	for _, e := range elems {
+		switch e := e.(type) {
+		case *dag.Spread:
+			d = demand.Union(d, demandForExpr(e.Expr))
+		case *dag.VectorValue:
+			d = demand.Union(d, demandForExpr(e.Expr))
+		default:
+			panic(e)
+		}
+	}
+	return d
+}
+
+func demandForAssignments(assignments []dag.Assignment, downstream demand.Demand) demand.Demand {
+	d := downstream
+	for _, a := range assignments {
+		if _, ok := a.LHS.(*dag.This); ok {
+			// Assignment clobbers a static field.
+			d = demand.Delete(d, demandForExpr(a.LHS))
+		} else {
+			// Add anything needed by a dynamic field.
+			d = demand.Union(d, demandForExpr(a.LHS))
 		}
-	default:
-		// Conservatively assume that `expr` uses it's entire input, regardless of output demand.
-		demandIn = demand.All()
+		d = demand.Union(d, demandForExpr(a.RHS))
 	}
-	return demandIn
+	return d
 }
diff --git a/compiler/optimizer/demand/demand.go b/compiler/optimizer/demand/demand.go
index 26f2a123b5..73b417a340 100644
--- a/compiler/optimizer/demand/demand.go
+++ b/compiler/optimizer/demand/demand.go
@@ -1,6 +1,10 @@
 package demand
 
-import "github.com/brimdata/super/pkg/field"
+import (
+	"maps"
+
+	"github.com/brimdata/super/pkg/field"
+)
 
 type Demand interface {
 	isDemand()
@@ -61,6 +65,35 @@ func Key(key string, value Demand) Demand {
 	return keys{key: value}
 }
 
+// Delete deletes entries in b from a.
+func Delete(a, b Demand) Demand {
+	aa, ok := a.(keys)
+	if !ok {
+		return a
+	}
+	bb, ok := b.(keys)
+	if !ok {
+		return a
+	}
+	copyOnWrite := true
+	for k, bv := range bb {
+		av, ok := aa[k]
+		if !ok {
+			continue
+		}
+		if copyOnWrite {
+			aa = maps.Clone(aa)
+			copyOnWrite = false
+		}
+		if IsAll(bv) {
+			delete(aa, k)
+			continue
+		}
+		aa[k] = Delete(av, bv)
+	}
+	return aa
+}
+
 func Union(a Demand, b Demand) Demand {
 	if _, ok := a.(all); ok {
 		return a
diff --git a/compiler/optimizer/optimizer.go b/compiler/optimizer/optimizer.go
index 053695bc16..5cbc0c7450 100644
--- a/compiler/optimizer/optimizer.go
+++ b/compiler/optimizer/optimizer.go
@@ -6,6 +6,7 @@ import (
 	"fmt"
 
 	"github.com/brimdata/super/compiler/dag"
+	"github.com/brimdata/super/compiler/optimizer/demand"
 	"github.com/brimdata/super/lake"
 	"github.com/brimdata/super/order"
 	"github.com/brimdata/super/pkg/field"
@@ -152,8 +153,8 @@ func (o *Optimizer) Optimize(seq dag.Seq) (dag.Seq, error) {
 	if err != nil {
 		return nil, err
 	}
-	seq = insertDemand(seq)
 	seq = removePassOps(seq)
+	DemandForSeq(seq, demand.All())
 	return seq, nil
 }
 
diff --git a/fuzz/fuzz.go b/fuzz/fuzz.go
index a596977ddb..39799674f3 100644
--- a/fuzz/fuzz.go
+++ b/fuzz/fuzz.go
@@ -115,8 +115,7 @@ func RunQuery(t testing.TB, zctx *super.Context, readers []zio.Reader, querySour
 		t.Skipf("%v", err)
 	}
 	if len(dag) > 0 {
-		demands := optimizer.InferDemandSeqOut(dag)
-		demand := demands[dag[0]]
+		demand := optimizer.DemandForSeq(dag, demand.All())
 		useDemand(demand)
 	}