diff --git a/reference/reference.go b/reference/reference.go
index d3088b68..f1d18035 100644
--- a/reference/reference.go
+++ b/reference/reference.go
@@ -8,12 +8,13 @@
 //	// repository.go
 //	repository			:= hostname ['/' component]+
 //	hostname 			:= hostcomponent [':' port-number]
-//	component			:= alpha-numeric [separator alpha-numeric]*
+//	component			:= subcomponent [separator subcomponent]*
+//	subcomponent			:= alpha-numeric ['-'* alpha-numeric]*
 //	hostcomponent                   := [hostpart '.']* hostpart
-// 	alpha-numeric			:= /[a-zA-Z0-9]+/
-//	separator			:= /[_-]/
+// 	alpha-numeric			:= /[a-z0-9]+/
+//	separator			:= /([_.]|__)/
 //	port-number			:= /[0-9]+/
-//	hostpart                        := /([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9-]*[a-zA-Z0-9])/
+//	hostpart                        := /([a-z0-9]|[a-z0-9][a-z0-9-]*[a-z0-9])/
 //
 //	// tag.go
 //	tag                             := /[\w][\w.-]{0,127}/
diff --git a/reference/regexp.go b/reference/regexp.go
index aa3480c5..579d5cda 100644
--- a/reference/regexp.go
+++ b/reference/regexp.go
@@ -3,14 +3,19 @@ package reference
 import "regexp"
 
 var (
+	// nameSubComponentRegexp defines the part of the name which must be
+	// begin and end with an alphanumeric character. These characters can
+	// be separated by any number of dashes.
+	nameSubComponentRegexp = regexp.MustCompile(`[a-z0-9]+(?:[-]+[a-z0-9]+)*`)
+
 	// nameComponentRegexp restricts registry path component names to
 	// start with at least one letter or number, with following parts able to
-	// be separated by one period, dash or underscore.
-	nameComponentRegexp = regexp.MustCompile(`[a-zA-Z0-9]+(?:[._-][a-z0-9]+)*`)
+	// be separated by one period, underscore or double underscore.
+	nameComponentRegexp = regexp.MustCompile(nameSubComponentRegexp.String() + `(?:(?:[._]|__)` + nameSubComponentRegexp.String() + `)*`)
 
 	nameRegexp = regexp.MustCompile(`(?:` + nameComponentRegexp.String() + `/)*` + nameComponentRegexp.String())
 
-	hostnameComponentRegexp = regexp.MustCompile(`(?:[a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9-]*[a-zA-Z0-9])`)
+	hostnameComponentRegexp = regexp.MustCompile(`(?:[a-z0-9]|[a-z0-9][a-z0-9-]*[a-z0-9])`)
 
 	// hostnameComponentRegexp restricts the registry hostname component of a repository name to
 	// start with a component as defined by hostnameRegexp and followed by an optional port.
diff --git a/reference/regexp_test.go b/reference/regexp_test.go
index 9435ee2a..530a6eb6 100644
--- a/reference/regexp_test.go
+++ b/reference/regexp_test.go
@@ -16,14 +16,14 @@ func checkRegexp(t *testing.T, r *regexp.Regexp, m regexpMatch) {
 	matches := r.FindStringSubmatch(m.input)
 	if m.match && matches != nil {
 		if len(matches) != (r.NumSubexp()+1) || matches[0] != m.input {
-			t.Fatalf("Bad match result: %#v", matches)
+			t.Fatalf("Bad match result %#v for %q", matches, m.input)
 		}
 		if len(matches) < (len(m.subs) + 1) {
-			t.Errorf("Expected %d sub matches, only have %d", len(m.subs), len(matches)-1)
+			t.Errorf("Expected %d sub matches, only have %d for %q", len(m.subs), len(matches)-1, m.input)
 		}
 		for i := range m.subs {
 			if m.subs[i] != matches[i+1] {
-				t.Errorf("Unexpected submatch %d: %q, expected %q", i+1, matches[i+1], m.subs[i])
+				t.Errorf("Unexpected submatch %d: %q, expected %q for %q", i+1, matches[i+1], m.subs[i], m.input)
 			}
 		}
 	} else if m.match {
@@ -325,6 +325,75 @@ func TestFullNameRegexp(t *testing.T) {
 			match: true,
 			subs:  []string{"xn--7o8h.com", "myimage"},
 		},
+		{
+			input: "example.com/xn--7o8h.com/myimage", // 🐳.com in punycode
+			match: true,
+			subs:  []string{"example.com", "xn--7o8h.com/myimage"},
+		},
+		{
+			input: "example.com/some_separator__underscore/myimage",
+			match: true,
+			subs:  []string{"example.com", "some_separator__underscore/myimage"},
+		},
+		{
+			input: "example.com/__underscore/myimage",
+			match: false,
+		},
+		{
+			input: "example.com/..dots/myimage",
+			match: false,
+		},
+		{
+			input: "example.com/.dots/myimage",
+			match: false,
+		},
+		{
+			input: "example.com/nodouble..dots/myimage",
+			match: false,
+		},
+		{
+			input: "example.com/nodouble..dots/myimage",
+			match: false,
+		},
+		{
+			input: "docker./docker",
+			match: false,
+		},
+		{
+			input: ".docker/docker",
+			match: false,
+		},
+		{
+			input: "docker-/docker",
+			match: false,
+		},
+		{
+			input: "-docker/docker",
+			match: false,
+		},
+		{
+			input: "do..cker/docker",
+			match: false,
+		},
+		{
+			input: "do__cker:8080/docker",
+			match: false,
+		},
+		{
+			input: "do__cker/docker",
+			match: true,
+			subs:  []string{"", "do__cker/docker"},
+		},
+		{
+			input: "b.gcr.io/test.example.com/my-app",
+			match: true,
+			subs:  []string{"b.gcr.io", "test.example.com/my-app"},
+		},
+		{
+			input: "registry.io/foo/project--id.module--name.ver---sion--name",
+			match: true,
+			subs:  []string{"registry.io", "foo/project--id.module--name.ver---sion--name"},
+		},
 	}
 	for i := range testcases {
 		checkRegexp(t, anchoredNameRegexp, testcases[i])