diff --git a/plugin/deepcopy/deepcopy.go b/plugin/deepcopy/deepcopy.go
index debf42d..2a4f4a6 100644
--- a/plugin/deepcopy/deepcopy.go
+++ b/plugin/deepcopy/deepcopy.go
@@ -369,7 +369,10 @@ func (g *gen) genField(fieldType types.Type, thisField, thatField string) error
 		p.P("%s = make(%s, len(%s))", thatField, g.TypeString(typ), thisField)
 		p.Out()
 		p.P("}") // not nil
-		if canCopy(typ.Elem()) {
+		named, isNamed := fieldType.(*types.Named)
+		if isNamed && hasDeepCopyMethod(named) {
+			p.P("%s.DeepCopy(%s)", wrap(thisField), thatField)
+		} else if canCopy(typ.Elem()) {
 			p.P("copy(%s, %s)", thatField, thisField)
 		} else {
 			p.P("%s(%s, %s)", g.GetFuncName(typ), thatField, thisField)
@@ -381,7 +384,12 @@ func (g *gen) genField(fieldType types.Type, thisField, thatField string) error
 		p.P("if %s != nil {", thisField)
 		p.In()
 		p.P("%s = make(%s, len(%s))", thatField, g.TypeString(typ), thisField)
-		p.P("%s(%s, %s)", g.GetFuncName(typ), thatField, thisField)
+		named, isNamed := fieldType.(*types.Named)
+		if isNamed && hasDeepCopyMethod(named) {
+			p.P("%s.DeepCopy(%s)", wrap(thisField), thatField)
+		} else {
+			p.P("%s(%s, %s)", g.GetFuncName(typ), thatField, thisField)
+		}
 		p.Out()
 		p.P("} else {")
 		p.In()
diff --git a/test/normal/deepcopy_test.go b/test/normal/deepcopy_test.go
index 79f04bd..43a1525 100644
--- a/test/normal/deepcopy_test.go
+++ b/test/normal/deepcopy_test.go
@@ -84,3 +84,22 @@ func TestDeepCopyMapNilEntry(t *testing.T) {
 		t.Fatalf("want %v got %v\n this = %#v, that = %#v\n", want, got, this, that)
 	}
 }
+
+func TestDeepCopyCustomMap(t *testing.T) {
+	this := customMap{
+		"a": "A",
+	}
+	that := customMap{}
+	deepcopy(this, that)
+	if that["a"] != "copy of A" {
+		t.Fatalf("expected use of customMap.DeepCopy")
+	}
+}
+
+type customMap map[string]string
+
+func (c customMap) DeepCopy(to customMap) {
+	for k, v := range c {
+		to[k] = "copy of " + v
+	}
+}