diff --git a/swarm/network/kademlia.go b/swarm/network/kademlia.go
index 1193e3b65..146f39106 100644
--- a/swarm/network/kademlia.go
+++ b/swarm/network/kademlia.go
@@ -628,7 +628,8 @@ func (k *Kademlia) string() string {
 // used for testing only
 // TODO move to separate testing tools file
 type PeerPot struct {
-	NNSet [][]byte
+	NNSet       [][]byte
+	PeersPerBin []int
 }
 
 // NewPeerPotMap creates a map of pot record of *BzzAddr with keys
@@ -654,6 +655,7 @@ func NewPeerPotMap(neighbourhoodSize int, addrs [][]byte) map[string]*PeerPot {
 
 		// all nn-peers
 		var nns [][]byte
+		peersPerBin := make([]int, depth)
 
 		// iterate through the neighbours, going from the deepest to the shallowest
 		np.EachNeighbour(a, Pof, func(val pot.Val, po int) bool {
@@ -667,14 +669,18 @@ func NewPeerPotMap(neighbourhoodSize int, addrs [][]byte) map[string]*PeerPot {
 			// a neighbor is any peer in or deeper than the depth
 			if po >= depth {
 				nns = append(nns, addr)
-				return true
+			} else {
+				// for peers < depth, we just count the number in each bin
+				// the bin is the index of the slice
+				peersPerBin[po]++
 			}
-			return false
+			return true
 		})
 
-		log.Trace(fmt.Sprintf("%x PeerPotMap NNS: %s", addrs[i][:4], LogAddrs(nns)))
+		log.Trace(fmt.Sprintf("%x PeerPotMap NNS: %s, peersPerBin", addrs[i][:4], LogAddrs(nns)))
 		ppmap[common.Bytes2Hex(a)] = &PeerPot{
-			NNSet: nns,
+			NNSet:       nns,
+			PeersPerBin: peersPerBin,
 		}
 	}
 	return ppmap
@@ -698,6 +704,39 @@ func (k *Kademlia) saturation() int {
 	return prev
 }
 
+// isSaturated returns true if the kademlia is considered saturated, or false if not.
+// It checks this by checking an array of ints called unsaturatedBins; each item in that array corresponds
+// to the bin which is unsaturated (number of connections < k.MinBinSize).
+// The bin is considered unsaturated only if there are actual peers in that PeerPot's bin (peersPerBin)
+// (if there is no peer for a given bin, then no connection could ever be established;
+// in a God's view this is relevant as no more peers will ever appear on that bin)
+func (k *Kademlia) isSaturated(peersPerBin []int, depth int) bool {
+	// depth could be calculated from k but as this is called from `GetHealthInfo()`,
+	// the depth has already been calculated so we can require it as a parameter
+
+	// early check for depth
+	if depth != len(peersPerBin) {
+		return false
+	}
+	unsaturatedBins := make([]int, 0)
+	k.conns.EachBin(k.base, Pof, 0, func(po, size int, f func(func(val pot.Val) bool) bool) bool {
+
+		if po >= depth {
+			return false
+		}
+		log.Trace("peers per bin", "peersPerBin[po]", peersPerBin[po], "po", po)
+		// if there are actually peers in the PeerPot who can fulfill k.MinBinSize
+		if size < k.MinBinSize && size < peersPerBin[po] {
+			log.Trace("connections for po", "po", po, "size", size)
+			unsaturatedBins = append(unsaturatedBins, po)
+		}
+		return true
+	})
+
+	log.Trace("list of unsaturated bins", "unsaturatedBins", unsaturatedBins)
+	return len(unsaturatedBins) == 0
+}
+
 // knowNeighbours tests if all neighbours in the peerpot
 // are found among the peers known to the kademlia
 // It is used in Healthy function for testing only
@@ -780,11 +819,13 @@ type Health struct {
 	ConnectNN        bool     // whether node is connected to all its neighbours
 	CountConnectNN   int      // amount of neighbours connected to
 	MissingConnectNN [][]byte // which neighbours we should have been connected to but we're not
-	Saturated        bool     // whether we are connected to all the peers we would have liked to
-	Hive             string
+	// Saturated: if in all bins < depth number of connections >= MinBinsize or,
+	// if number of connections < MinBinSize, to the number of available peers in that bin
+	Saturated bool
+	Hive      string
 }
 
-// Healthy reports the health state of the kademlia connectivity
+// GetHealthInfo reports the health state of the kademlia connectivity
 //
 // The PeerPot argument provides an all-knowing view of the network
 // The resulting Health object is a result of comparisons between
@@ -792,7 +833,7 @@ type Health struct {
 // what SHOULD it have been when we take all we know about the network into consideration.
 //
 // used for testing only
-func (k *Kademlia) Healthy(pp *PeerPot) *Health {
+func (k *Kademlia) GetHealthInfo(pp *PeerPot) *Health {
 	k.lock.RLock()
 	defer k.lock.RUnlock()
 	if len(pp.NNSet) < k.NeighbourhoodSize {
@@ -801,7 +842,10 @@ func (k *Kademlia) Healthy(pp *PeerPot) *Health {
 	gotnn, countgotnn, culpritsgotnn := k.connectedNeighbours(pp.NNSet)
 	knownn, countknownn, culpritsknownn := k.knowNeighbours(pp.NNSet)
 	depth := depthForPot(k.conns, k.NeighbourhoodSize, k.base)
-	saturated := k.saturation() < depth
+
+	// check saturation
+	saturated := k.isSaturated(pp.PeersPerBin, depth)
+
 	log.Trace(fmt.Sprintf("%08x: healthy: knowNNs: %v, gotNNs: %v, saturated: %v\n", k.base, knownn, gotnn, saturated))
 	return &Health{
 		KnowNN:           knownn,
@@ -814,3 +858,13 @@ func (k *Kademlia) Healthy(pp *PeerPot) *Health {
 		Hive:             k.string(),
 	}
 }
+
+// Healthy return the strict interpretation of `Healthy` given a `Health` struct
+// definition of strict health: all conditions must be true:
+// - we at least know one peer
+// - we know all neighbors
+// - we are connected to all known neighbors
+// - it is saturated
+func (h *Health) Healthy() bool {
+	return h.KnowNN && h.ConnectNN && h.CountKnowNN > 0 && h.Saturated
+}
diff --git a/swarm/network/kademlia_test.go b/swarm/network/kademlia_test.go
index 8a724756b..b4663eee5 100644
--- a/swarm/network/kademlia_test.go
+++ b/swarm/network/kademlia_test.go
@@ -168,6 +168,46 @@ func TestNeighbourhoodDepth(t *testing.T) {
 	testNum++
 }
 
+// TestHighMinBinSize tests that the saturation function also works
+// if MinBinSize is > 2, the connection count is < k.MinBinSize
+// and there are more peers available than connected
+func TestHighMinBinSize(t *testing.T) {
+	// a function to test for different MinBinSize values
+	testKad := func(minBinSize int) {
+		// create a test kademlia
+		tk := newTestKademlia(t, "11111111")
+		// set its MinBinSize to desired value
+		tk.KadParams.MinBinSize = minBinSize
+
+		// add a couple of peers (so we have NN and depth)
+		tk.On("00000000") // bin 0
+		tk.On("11100000") // bin 3
+		tk.On("11110000") // bin 4
+
+		first := "10000000" // add a first peer at bin 1
+		tk.Register(first)  // register it
+		// we now have one registered peer at bin 1;
+		// iterate and connect one peer at each iteration;
+		// should be unhealthy until at minBinSize - 1
+		// we connect the unconnected but registered peer
+		for i := 1; i < minBinSize; i++ {
+			peer := fmt.Sprintf("1000%b", 8|i)
+			tk.On(peer)
+			if i == minBinSize-1 {
+				tk.On(first)
+				tk.checkHealth(true)
+				return
+			}
+			tk.checkHealth(false)
+		}
+	}
+	// test MinBinSizes of 3 to 5
+	testMinBinSizes := []int{3, 4, 5}
+	for _, k := range testMinBinSizes {
+		testKad(k)
+	}
+}
+
 // TestHealthStrict tests the simplest definition of health
 // Which means whether we are connected to all neighbors we know of
 func TestHealthStrict(t *testing.T) {
@@ -176,60 +216,116 @@ func TestHealthStrict(t *testing.T) {
 	// no peers
 	// unhealthy (and lonely)
 	tk := newTestKademlia(t, "11111111")
-	tk.checkHealth(false, false)
+	tk.checkHealth(false)
 
 	// know one peer but not connected
 	// unhealthy
 	tk.Register("11100000")
-	tk.checkHealth(false, false)
+	tk.checkHealth(false)
 
 	// know one peer and connected
-	// healthy
+	// unhealthy: not saturated
 	tk.On("11100000")
-	tk.checkHealth(true, false)
+	tk.checkHealth(true)
 
 	// know two peers, only one connected
 	// unhealthy
 	tk.Register("11111100")
-	tk.checkHealth(false, false)
+	tk.checkHealth(false)
 
 	// know two peers and connected to both
 	// healthy
 	tk.On("11111100")
-	tk.checkHealth(true, false)
+	tk.checkHealth(true)
 
 	// know three peers, connected to the two deepest
 	// healthy
 	tk.Register("00000000")
-	tk.checkHealth(true, false)
+	tk.checkHealth(false)
 
 	// know three peers, connected to all three
 	// healthy
 	tk.On("00000000")
-	tk.checkHealth(true, false)
+	tk.checkHealth(true)
 
 	// add fourth peer deeper than current depth
 	// unhealthy
 	tk.Register("11110000")
-	tk.checkHealth(false, false)
+	tk.checkHealth(false)
 
 	// connected to three deepest peers
 	// healthy
 	tk.On("11110000")
-	tk.checkHealth(true, false)
+	tk.checkHealth(true)
 
 	// add additional peer in same bin as deepest peer
 	// unhealthy
 	tk.Register("11111101")
-	tk.checkHealth(false, false)
+	tk.checkHealth(false)
 
 	// four deepest of five peers connected
 	// healthy
 	tk.On("11111101")
-	tk.checkHealth(true, false)
+	tk.checkHealth(true)
+
+	// add additional peer in bin 0
+	// unhealthy: unsaturated bin 0, 2 known but 1 connected
+	tk.Register("00000001")
+	tk.checkHealth(false)
+
+	// Connect second in bin 0
+	// healthy
+	tk.On("00000001")
+	tk.checkHealth(true)
+
+	// add peer in bin 1
+	// unhealthy, as it is known but not connected
+	tk.Register("10000000")
+	tk.checkHealth(false)
+
+	// connect  peer in bin 1
+	// depth change, is now 1
+	// healthy, 1 peer in bin 1 known and connected
+	tk.On("10000000")
+	tk.checkHealth(true)
+
+	// add second peer in bin 1
+	// unhealthy, as it is known but not connected
+	tk.Register("10000001")
+	tk.checkHealth(false)
+
+	// connect second peer in bin 1
+	// healthy,
+	tk.On("10000001")
+	tk.checkHealth(true)
+
+	// connect third peer in bin 1
+	// healthy,
+	tk.On("10000011")
+	tk.checkHealth(true)
+
+	// add peer in bin 2
+	// unhealthy, no depth change
+	tk.Register("11000000")
+	tk.checkHealth(false)
+
+	// connect peer in bin 2
+	// depth change - as we already have peers in bin 3 and 4,
+	// we have contiguous bins, no bin < po 5 is empty -> depth 5
+	// healthy, every bin < depth has the max available peers,
+	// even if they are < MinBinSize
+	tk.On("11000000")
+	tk.checkHealth(true)
+
+	// add peer in bin 2
+	// unhealthy, peer bin is below depth 5 but
+	// has more available peers (2) than connected ones (1)
+	// --> unsaturated
+	tk.Register("11000011")
+	tk.checkHealth(false)
 }
 
-func (tk *testKademlia) checkHealth(expectHealthy bool, expectSaturation bool) {
+func (tk *testKademlia) checkHealth(expectHealthy bool) {
 	tk.t.Helper()
 	kid := common.Bytes2Hex(tk.BaseAddr())
 	addrs := [][]byte{tk.BaseAddr()}
@@ -239,13 +335,13 @@ func (tk *testKademlia) checkHealth(expectHealthy bool, expectSaturation bool) {
 	})
 
 	pp := NewPeerPotMap(tk.NeighbourhoodSize, addrs)
-	healthParams := tk.Healthy(pp[kid])
+	healthParams := tk.GetHealthInfo(pp[kid])
 
 	// definition of health, all conditions but be true:
 	// - we at least know one peer
 	// - we know all neighbors
 	// - we are connected to all known neighbors
-	health := healthParams.KnowNN && healthParams.ConnectNN && healthParams.CountKnowNN > 0
+	health := healthParams.Healthy()
 	if expectHealthy != health {
 		tk.t.Fatalf("expected kademlia health %v, is %v\n%v", expectHealthy, health, tk.String())
 	}
diff --git a/swarm/network/simulation/kademlia.go b/swarm/network/simulation/kademlia.go
index 6d8d0e0a2..c58d402b0 100644
--- a/swarm/network/simulation/kademlia.go
+++ b/swarm/network/simulation/kademlia.go
@@ -64,7 +64,7 @@ func (s *Simulation) WaitTillHealthy(ctx context.Context) (ill map[enode.ID]*net
 				addr := common.Bytes2Hex(k.BaseAddr())
 				pp := ppmap[addr]
 				//call Healthy RPC
-				h := k.Healthy(pp)
+				h := k.GetHealthInfo(pp)
 				//print info
 				log.Debug(k.String())
 				log.Debug("kademlia", "connectNN", h.ConnectNN, "knowNN", h.KnowNN)
diff --git a/swarm/network/simulations/discovery/discovery_test.go b/swarm/network/simulations/discovery/discovery_test.go
index 86aa6f6dd..5227de3bb 100644
--- a/swarm/network/simulations/discovery/discovery_test.go
+++ b/swarm/network/simulations/discovery/discovery_test.go
@@ -267,7 +267,7 @@ func discoverySimulation(nodes, conns int, adapter adapters.NodeAdapter) (*simul
 		}
 
 		healthy := &network.Health{}
-		if err := client.Call(&healthy, "hive_healthy", ppmap[common.Bytes2Hex(id.Bytes())]); err != nil {
+		if err := client.Call(&healthy, "hive_getHealthInfo", ppmap[common.Bytes2Hex(id.Bytes())]); err != nil {
 			return false, fmt.Errorf("error getting node health: %s", err)
 		}
 		log.Debug(fmt.Sprintf("node %4s healthy: connected nearest neighbours: %v, know nearest neighbours: %v,\n\n%v", id, healthy.ConnectNN, healthy.KnowNN, healthy.Hive))
@@ -352,7 +352,7 @@ func discoveryPersistenceSimulation(nodes, conns int, adapter adapters.NodeAdapt
 				healthy := &network.Health{}
 				addr := id.String()
 				ppmap := network.NewPeerPotMap(network.NewKadParams().NeighbourhoodSize, addrs)
-				if err := client.Call(&healthy, "hive_healthy", ppmap[common.Bytes2Hex(id.Bytes())]); err != nil {
+				if err := client.Call(&healthy, "hive_getHealthInfo", ppmap[common.Bytes2Hex(id.Bytes())]); err != nil {
 					return fmt.Errorf("error getting node health: %s", err)
 				}
 
@@ -422,7 +422,7 @@ func discoveryPersistenceSimulation(nodes, conns int, adapter adapters.NodeAdapt
 		healthy := &network.Health{}
 		ppmap := network.NewPeerPotMap(network.NewKadParams().NeighbourhoodSize, addrs)
 
-		if err := client.Call(&healthy, "hive_healthy", ppmap[common.Bytes2Hex(id.Bytes())]); err != nil {
+		if err := client.Call(&healthy, "hive_getHealthInfo", ppmap[common.Bytes2Hex(id.Bytes())]); err != nil {
 			return false, fmt.Errorf("error getting node health: %s", err)
 		}
 		log.Info(fmt.Sprintf("node %4s healthy: got nearest neighbours: %v, know nearest neighbours: %v", id, healthy.ConnectNN, healthy.KnowNN))