diff --git a/x/model/name.go b/x/model/name.go
index ff74668c..ccc80ad4 100644
--- a/x/model/name.go
+++ b/x/model/name.go
@@ -262,6 +262,44 @@ func (r Name) Complete() bool {
 	return !slices.Contains(r.Parts(), "")
 }
 
+// EqualFold reports whether r and o are equivalent model names, ignoring
+// case.
+func (r Name) EqualFold(o Name) bool {
+	return r.CompareFold(o) == 0
+}
+
+// CompareFold performs a case-insensitive comparison of two Names. It returns
+// an integer comparing two Names lexicographically. The result will be 0 if
+// r == o, -1 if r < o, and +1 if r > o.
+//
+// This can be used with [slice.SortFunc].
+func (r Name) CompareFold(o Name) int {
+	return cmp.Or(
+		compareFold(r.host, o.host),
+		compareFold(r.namespace, o.namespace),
+		compareFold(r.model, o.model),
+		compareFold(r.tag, o.tag),
+		compareFold(r.build, o.build),
+	)
+}
+
+func compareFold(a, b string) int {
+	for i := 0; i < len(a) && i < len(b); i++ {
+		ca, cb := downcase(a[i]), downcase(b[i])
+		if n := cmp.Compare(ca, cb); n != 0 {
+			return n
+		}
+	}
+	return cmp.Compare(len(a), len(b))
+}
+
+func downcase(c byte) byte {
+	if c >= 'A' && c <= 'Z' {
+		return c + 'a' - 'A'
+	}
+	return c
+}
+
 // TODO(bmizerany): Compare
 // TODO(bmizerany): MarshalText/UnmarshalText
 // TODO(bmizerany): LogValue
@@ -280,12 +318,6 @@ func (r Name) Parts() []string {
 	}
 }
 
-// EqualFold reports whether r and o are equivalent model names, ignoring
-// case.
-func (r Name) EqualFold(o Name) bool {
-	return r.MapHash() == o.MapHash()
-}
-
 // Parts returns a sequence of the parts of a Name string from most specific
 // to least specific.
 //
diff --git a/x/model/name_test.go b/x/model/name_test.go
index 63c5676c..73359987 100644
--- a/x/model/name_test.go
+++ b/x/model/name_test.go
@@ -2,6 +2,7 @@ package model
 
 import (
 	"fmt"
+	"slices"
 	"strings"
 	"testing"
 )
@@ -339,4 +340,23 @@ func ExampleName_MapHash() {
 	// 2
 }
 
+func ExampleName_CompareFold_sort() {
+	names := []Name{
+		ParseName("mistral:latest"),
+		ParseName("mistRal:7b+q4"),
+		ParseName("MIstral:7b"),
+	}
+
+	slices.SortFunc(names, Name.CompareFold)
+
+	for _, n := range names {
+		fmt.Println(n)
+	}
+
+	// Output:
+	// MIstral:7b
+	// mistRal:7b+q4
+	// mistral:latest
+}
+
 func keep[T any](v T) T { return v }