diff --git a/checker/cost.go b/checker/cost.go
index b9cd8a2ed..59be751c9 100644
--- a/checker/cost.go
+++ b/checker/cost.go
@@ -930,6 +930,9 @@ func (c *coster) computeSize(e ast.Expr) *SizeEstimate {
 	if size, ok := c.computedSizes[e.ID()]; ok {
 		return &size
 	}
+	if size := computeExprSize(e); size != nil {
+		return size
+	}
 	// Ensure size estimates are computed first as users may choose to override the costs that
 	// CEL would otherwise ascribe to the type.
 	node := astNode{expr: e, path: c.getPath(e), t: c.getType(e)}
@@ -938,9 +941,6 @@ func (c *coster) computeSize(e ast.Expr) *SizeEstimate {
 		c.computedSizes[e.ID()] = *size
 		return size
 	}
-	if size := computeExprSize(e); size != nil {
-		return size
-	}
 	if size := computeTypeSize(c.getType(e)); size != nil {
 		return size
 	}
diff --git a/checker/cost_test.go b/checker/cost_test.go
index 2bec0e94a..f667ebe0e 100644
--- a/checker/cost_test.go
+++ b/checker/cost_test.go
@@ -715,6 +715,31 @@ func TestCost(t *testing.T) {
 			expr:   `self.val1 == 1.0`,
 			wanted: FixedCostEstimate(3),
 		},
+		{
+			name: "bytes list max",
+			expr: "[bytes('012345678901'), bytes('012345678901'), bytes('012345678901'), bytes('012345678901'), bytes('012345678901')].max()",
+			options: []CostOption{
+				OverloadCostEstimate("list_bytes_max",
+					func(estimator CostEstimator, target *AstNode, args []AstNode) *CallEstimate {
+						if target != nil {
+							// Charge 1 cost for comparing each element in the list
+							elCost := CostEstimate{Min: 1, Max: 1}
+							// If the list contains strings or bytes, add the cost of traversing all the strings/bytes as a way
+							// of estimating the additional comparison cost.
+							if elNode := listElementNode(*target); elNode != nil {
+								k := elNode.Type().Kind()
+								if k == types.StringKind || k == types.BytesKind {
+									sz := sizeEstimate(estimator, elNode)
+									elCost = elCost.Add(sz.MultiplyByCostFactor(common.StringTraversalCostFactor))
+								}
+								return &CallEstimate{CostEstimate: sizeEstimate(estimator, *target).MultiplyByCost(elCost)}
+							}
+						}
+						return nil
+					}),
+			},
+			wanted: CostEstimate{Min: 25, Max: 35},
+		},
 	}
 
 	for _, tst := range cases {
@@ -745,6 +770,14 @@ func TestCost(t *testing.T) {
 			if err != nil {
 				t.Fatalf("environment creation error: %v", err)
 			}
+			maxFunc, _ := decls.NewFunction("max",
+				decls.MemberOverload("list_bytes_max",
+					[]*types.Type{types.NewListType(types.BytesType)},
+					types.BytesType))
+			err = e.AddFunctions(maxFunc)
+			if err != nil {
+				t.Fatalf("environment creation error: %v", err)
+			}
 			err = e.AddIdents(tc.vars...)
 			if err != nil {
 				t.Fatalf("environment creation error: %s\n", err)
@@ -773,6 +806,9 @@ func (tc testCostEstimator) EstimateSize(element AstNode) *SizeEstimate {
 	if l, ok := tc.hints[strings.Join(element.Path(), ".")]; ok {
 		return &SizeEstimate{Min: 0, Max: l}
 	}
+	if element.Type() == types.BytesType {
+		return &SizeEstimate{Min: 0, Max: 12}
+	}
 	return nil
 }
 
@@ -793,3 +829,32 @@ func estimateSize(estimator CostEstimator, node AstNode) SizeEstimate {
 	}
 	return SizeEstimate{Min: 0, Max: math.MaxUint64}
 }
+
+func listElementNode(list AstNode) AstNode {
+	if params := list.Type().Parameters(); len(params) > 0 {
+		lt := params[0]
+		nodePath := list.Path()
+		if nodePath != nil {
+			// Provide path if we have it so that a OpenAPIv3 maxLength validation can be looked up, if it exists
+			// for this node.
+			path := make([]string, len(nodePath)+1)
+			copy(path, nodePath)
+			path[len(nodePath)] = "@items"
+			return &astNode{path: path, t: lt, expr: nil}
+		} else {
+			// Provide just the type if no path is available so that worst case size can be looked up based on type.
+			return &astNode{t: lt, expr: nil}
+		}
+	}
+	return nil
+}
+
+func sizeEstimate(estimator CostEstimator, t AstNode) SizeEstimate {
+	if sz := t.ComputedSize(); sz != nil {
+		return *sz
+	}
+	if sz := estimator.EstimateSize(t); sz != nil {
+		return *sz
+	}
+	return SizeEstimate{Min: 0, Max: math.MaxUint64}
+}