diff --git a/capability/policy/match.go b/capability/policy/match.go
index d6aaa7a..6da07ca 100644
--- a/capability/policy/match.go
+++ b/capability/policy/match.go
@@ -11,11 +11,16 @@ import (
 	"github.com/ucan-wg/go-ucan/capability/policy/selector"
 )
 
-// Filter extracts a subset of the policy related to the specified selector.
 func (p Policy) Filter(sel selector.Selector) Policy {
+	return p.FilterWithMatcher(sel, selector.SegmentEquals)
+}
+
+// FilterWithMatcher extracts a subset of the policy related to the specified selector,
+// by matching each segment using the given selector.SegmentMatcher.
+func (p Policy) FilterWithMatcher(sel selector.Selector, matcher selector.SegmentMatcher) Policy {
 	var filtered Policy
 	for _, stmt := range p {
-		if stmt.Selector().Matches(sel) {
+		if stmt.Selector().Matches(sel, matcher) {
 			filtered = append(filtered, stmt)
 		}
 	}
diff --git a/capability/policy/match_test.go b/capability/policy/match_test.go
index 549e211..7ea0bcf 100644
--- a/capability/policy/match_test.go
+++ b/capability/policy/match_test.go
@@ -563,6 +563,21 @@ func TestPolicyFilter(t *testing.T) {
 	sel3 := selector.Selector{selector.NewFieldSegment("nonexistent")}
 	filtered = p.Filter(sel3)
 	assert.Len(t, filtered, 0)
+
+	stmt1 = Equal(
+		selector.Selector{selector.NewFieldSegment(".http.host")},
+		basicnode.NewString("mainnet.infura.io"),
+	)
+	stmt2, err := Like(
+		selector.Selector{selector.NewFieldSegment(".jsonrpc.method")},
+		"eth_*",
+	)
+	require.NoError(t, err)
+
+	p = Policy{stmt1, stmt2}
+	filtered = p.FilterWithMatcher(selector.Selector{selector.NewFieldSegment(".http")}, selector.SegmentStartsWith)
+	assert.Len(t, filtered, 1)
+	assert.Equal(t, stmt1, filtered[0])
 }
 
 func FuzzPolicyFilter(f *testing.F) {
diff --git a/capability/policy/selector/selector.go b/capability/policy/selector/selector.go
index ed2a0f8..9437d59 100644
--- a/capability/policy/selector/selector.go
+++ b/capability/policy/selector/selector.go
@@ -24,13 +24,13 @@ func (s Selector) String() string {
 }
 
 // Matches checks if the selector matches another selector.
-func (s Selector) Matches(other Selector) bool {
+func (s Selector) Matches(other Selector, matcher SegmentMatcher) bool {
 	if len(s) != len(other) {
 		return false
 	}
 
 	for i, seg := range s {
-		if seg.str != other[i].str {
+		if !matcher(seg, other[i]) {
 			return false
 		}
 	}
@@ -88,6 +88,16 @@ func NewIteratorSegment() segment {
 	}
 }
 
+type SegmentMatcher func(s1, s2 segment) bool
+
+var SegmentEquals SegmentMatcher = func(s1, s2 segment) bool {
+	return s1.str == s2.str
+}
+
+var SegmentStartsWith SegmentMatcher = func(s1, s2 segment) bool {
+	return strings.HasPrefix(s1.str, s2.str)
+}
+
 // String returns the segment's string representation.
 func (s segment) String() string {
 	return s.str