diff --git a/ipam/ring/entry.go b/ipam/ring/entry.go
index b4774f8f..f82378fc 100644
--- a/ipam/ring/entry.go
+++ b/ipam/ring/entry.go
@@ -14,8 +14,7 @@ type entry struct {
 	Token   address.Address // The start of this range
 	Peer    mesh.PeerName   // Who owns this range
 	Version uint32          // Version of this range
-	Free    address.Offset  // Number of free IPs in this range
-	// Note: Free should perhaps be an address.Count, but we can't change the wire protocol
+	Free    address.Count   // Number of free IPs in this range
 }
 
 func (e *entry) Equal(e2 *entry) bool {
@@ -23,7 +22,7 @@ func (e *entry) Equal(e2 *entry) bool {
 		e.Version == e2.Version
 }
 
-func (e *entry) update(peername mesh.PeerName, free address.Offset) {
+func (e *entry) update(peername mesh.PeerName, free address.Count) {
 	e.Peer = peername
 	e.Version++
 	e.Free = free
diff --git a/ipam/ring/ring.go b/ipam/ring/ring.go
index a8c6ae68..a9cf60dd 100644
--- a/ipam/ring/ring.go
+++ b/ipam/ring/ring.go
@@ -109,12 +109,12 @@ func (r *Ring) Range() address.Range {
 
 // Returns the distance between two tokens on this ring, dealing
 // with ranges which cross the origin
-func (r *Ring) distance(start, end address.Address) address.Offset {
+func (r *Ring) distance(start, end address.Address) address.Count {
 	if end > start {
-		return address.Offset(end - start)
+		return address.Count(end - start)
 	}
 
-	return address.Offset((r.End - start) + (end - r.Start))
+	return address.Count((r.End - start) + (end - r.Start))
 }
 
 // GrantRangeToHost modifies the ring such that range [start, end)
@@ -375,12 +375,12 @@ func (r *Ring) ClaimForPeers(peers []mesh.PeerName) {
 	defer r.updateExportedVariables()
 
 	totalSize := r.distance(r.Start, r.End)
-	share := totalSize/address.Offset(len(peers)) + 1
-	remainder := totalSize % address.Offset(len(peers))
+	share := totalSize/address.Count(len(peers)) + 1
+	remainder := totalSize % address.Count(len(peers))
 	pos := r.Start
 
 	for i, peer := range peers {
-		if address.Offset(i) == remainder {
+		if address.Count(i) == remainder {
 			share--
 			if share == 0 {
 				break
@@ -450,11 +450,11 @@ func (r *Ring) ReportFree(freespace map[address.Address]address.Count) {
 		maxSize := r.distance(entry.Token, next.Token)
 		common.Assert(free <= address.Count(maxSize))
 
-		if address.Count(entries[i].Free) == free {
+		if entries[i].Free == free {
 			return
 		}
 
-		entries[i].Free = address.Offset(free)
+		entries[i].Free = free
 		entries[i].Version++
 	}
 }
@@ -473,7 +473,7 @@ func (ws weightedPeers) Swap(i, j int)      { ws[i], ws[j] = ws[j], ws[i] }
 // ChoosePeersToAskForSpace returns all peers we can ask for space in
 // the range [start, end), in weighted-random order.  Assumes start<end.
 func (r *Ring) ChoosePeersToAskForSpace(start, end address.Address) []mesh.PeerName {
-	totalSpacePerPeer := make(map[mesh.PeerName]address.Offset)
+	totalSpacePerPeer := make(map[mesh.PeerName]address.Count)
 
 	// iterate through tokens
 	for i, entry := range r.Entries {
diff --git a/net/address/address.go b/net/address/address.go
index b6e992ba..42aa3cc2 100644
--- a/net/address/address.go
+++ b/net/address/address.go
@@ -151,7 +151,7 @@ func Length(a, b Address) Count {
 	return Count(a - b)
 }
 
-func Min(a, b Offset) Offset {
+func Min(a, b Count) Count {
 	if a > b {
 		return b
 	}