diff --git a/code/sonalyze/table/hosts.go b/code/sonalyze/table/hosts.go
index 6bef0ea2..0bb988fa 100644
--- a/code/sonalyze/table/hosts.go
+++ b/code/sonalyze/table/hosts.go
@@ -248,44 +248,15 @@ func (h *Hostnames) HasElement(hostname string) bool {
 }
 
 func (this *Hostnames) Equal(that *Hostnames) bool {
-	return setCompare(this, that) == 0
+	return compare(this.s.sources, that.s.sources) == 0
 }
 
-// A > B if we can traverse B and A together and reach every node in A that is in B.
-//
-// A >= B if A > B or A = B.
-//
-// A = B if we can traverse B and A together and reach every node in A that is in B, and if from the
-// terminal nodes of that traversal we can continue to walk down the graph to the sinks and we reach
-// all the sinks that way.
-//
-// This is equivalent to saying that when we at every node of A that is reached by members of B,
-// every outgoing edge is touched, and there are no members of B that do not touch an outgoing edge,
-// or in other words, the set of first elements of B equals (in the normal sense) the set of first
-// elements of A.
-//
-// Consider A = {a.b, a.c, b.x} and B = {a}.  At level 1, A has two outgoing edges, for a and b.  B
-// touches only one of them, and B is therefore a subset, not equal.
-//
-// It could be that we just need to be talking about the set of leading elements of a and b... that
-// would be a blessing.
-
 func (a *Hostnames) HasSubset(b *Hostnames, proper bool) bool {
+	r := compare(a.s.sources, b.s.sources)
 	if proper {
-		return properSubset(a.s, b.s)
+		return r < 0
 	}
-	return false
-}
-
-func properSubset(a, b *set) bool {
-	return false
-}
-
-// This checks whether `that` is a subset of `this`, equal to `this`, or neither (superset or
-// incomparable).  It returns -1 for the first, 0 for the second, and 1 for the last.
-
-func setCompare(this, that *Hostnames) int {
-	panic("NYI")
+	return r <= 0
 }
 
 // Returns a string that is a comma-separated lists of the first elements of all the hosts in the
diff --git a/code/sonalyze/table/hosts_test.go b/code/sonalyze/table/hosts_test.go
index 2eebff00..d7df9cbf 100644
--- a/code/sonalyze/table/hosts_test.go
+++ b/code/sonalyze/table/hosts_test.go
@@ -65,6 +65,15 @@ func TestSetEquality(t *testing.T) {
 		t.Fatal("equal")
 	}
 
+	// a is a prefix of a.b.c and a.b.d so s = r
+	// s = {a.b.c, a.b.d}
+	// r = {a}
+	r := makeSet()
+	r.addNames("a")
+	if compare(s.sources, r.sources) != 0 {
+		t.Fatal("Equal")
+	}
+
 	// a.b is a prefix of a.b.c and a.b.d so s = q
 	// s = {a.b.c, a.b.d}
 	// q = {a.b}
@@ -81,22 +90,36 @@ func TestSetEquality(t *testing.T) {
 }
 
 func TestSetInequality(t *testing.T) {
-	s := makeSet()
-	s.addNames("a.b.c", "a.b.d", "b.e")
-	q := makeSet()
-	q.addNames("a.b")
+	{
+		s := makeSet()
+		s.addNames("a.b.c", "a.b.d", "b.e")
+		q := makeSet()
+		q.addNames("a.b")
 
-	// q < s
-	// s = {a.b.c, a.b.d, b.e}
-	// q = {a.b}
-	s.addNames("b.e")
-	if compare(s.sources, q.sources) >= 0 {
-		t.Fatal("Less")
+		// q < s
+		// s = {a.b.c, a.b.d, b.e}
+		// q = {a.b}
+		s.addNames("b.e")
+		if compare(s.sources, q.sources) >= 0 {
+			t.Fatal("Less")
+		}
+
+		// Same, but reversed - easy
+		if compare(q.sources, s.sources) != 1 {
+			t.Fatal("Not less")
+		}
 	}
 
-	// Same, but reversed - easy
-	if compare(q.sources, s.sources) != 1 {
-		t.Fatal("Not less")
+	{
+		// Harder: we diverge deeper down
+		s := makeSet()
+		s.addNames("a.b.c", "a.b.d")
+		q := makeSet()
+		q.addNames("a.b.c")
+
+		if compare(s.sources, q.sources) >= 0 {
+			t.Fatal("Less")
+		}
 	}
 }
 
@@ -172,4 +195,43 @@ func TestHostnames(t *testing.T) {
 	if !h.HasElement("a.b.c.e") {
 		t.Fatal("a.b.c.e")
 	}
+
+	{
+		lhs := NewHostnames()
+		lhs.Add("a.b.c")
+		lhs.Add("a.b.d")
+		rhs := NewHostnames()
+		rhs.Add("a.b")
+		if !lhs.Equal(rhs) {
+			t.Fatal("Equal")
+		}
+		if !lhs.HasSubset(rhs, false) {
+			t.Fatal("Equal")
+		}
+		if rhs.Equal(lhs) {
+			t.Fatal("Unequal")
+		}
+		if rhs.HasSubset(lhs, false) {
+			t.Fatal("Unequal")
+		}
+	}
+
+	{
+		lhs := NewHostnames()
+		lhs.Add("a.b.c")
+		lhs.Add("a.b.d")
+		rhs := NewHostnames()
+		rhs.Add("a.b.c")
+
+		if lhs.Equal(rhs) {
+			t.Fatal("Unequal")
+		}
+		if !lhs.HasSubset(rhs, true) {
+			t.Fatal("Less")
+		}
+		if rhs.HasSubset(lhs, true) {
+			t.Fatal("Less")
+		}
+	}
+
 }