diff --git a/probe/kubernetes/reporter.go b/probe/kubernetes/reporter.go
index 519c5ba115..bda02378dc 100644
--- a/probe/kubernetes/reporter.go
+++ b/probe/kubernetes/reporter.go
@@ -2,6 +2,7 @@ package kubernetes
 
 import (
 	"fmt"
+	"net"
 	"strings"
 
 	"k8s.io/apimachinery/pkg/labels"
@@ -294,23 +295,32 @@ func (r *Reporter) serviceTopology() (report.Topology, []Service, error) {
 	return result, services, err
 }
 
-// FIXME: Hideous hack to remove persistent-connection edges to virtual service
-//        IPs attributed to the internet. We add each service IP as a /32 network
-//        (the global service-cluster-ip-range is not exposed by the API
-//        server so we treat each IP as a /32 network see
-//        https://github.com/kubernetes/kubernetes/issues/25533).
-//        The right way of fixing this is performing DNAT mapping on persistent
-//        connections for which we don't have a robust solution
-//        (see https://github.com/weaveworks/scope/issues/1491)
+// FIXME: Hideous hack to remove persistent-connection edges to
+// virtual service IPs attributed to the internet. The global
+// service-cluster-ip-range is not exposed by the API server (see
+// https://github.com/kubernetes/kubernetes/issues/25533), so instead
+// we synthesise it by computing the smallest network that contains
+// all service IPs. That network may be smaller than the actual range
+// but that is ok, since in the end all we care about is that it
+// contains all the service IPs.
+//
+// The right way of fixing this is performing DNAT mapping on
+// persistent connections for which we don't have a robust solution
+// (see https://github.com/weaveworks/scope/issues/1491).
 func (r *Reporter) hostTopology(services []Service) report.Topology {
-	localNetworks := report.MakeStringSet()
+	serviceIPs := make([]net.IP, 0, len(services))
 	for _, service := range services {
-		localNetworks = localNetworks.Add(service.ClusterIP() + "/32")
+		if ip := net.ParseIP(service.ClusterIP()).To4(); ip != nil {
+			serviceIPs = append(serviceIPs, ip)
+		}
+	}
+	serviceNetwork := report.ContainingIPv4Network(serviceIPs)
+	if serviceNetwork == nil {
+		return report.MakeTopology()
 	}
-	node := report.MakeNode(report.MakeHostNodeID(r.hostID))
-	node = node.WithSets(report.MakeSets().
-		Add(host.LocalNetworks, localNetworks))
-	return report.MakeTopology().AddNode(node)
+	return report.MakeTopology().AddNode(
+		report.MakeNode(report.MakeHostNodeID(r.hostID)).
+			WithSets(report.MakeSets().Add(host.LocalNetworks, report.MakeStringSet(serviceNetwork.String()))))
 }
 
 func (r *Reporter) deploymentTopology(probeID string) (report.Topology, []Deployment, error) {
diff --git a/report/networks.go b/report/networks.go
index 4cd9d4a9b0..819219d028 100644
--- a/report/networks.go
+++ b/report/networks.go
@@ -105,3 +105,70 @@ func ipv4Nets(addrs []net.Addr) []*net.IPNet {
 	}
 	return nets
 }
+
+// ContainingIPv4Network determines the smallest network containing
+// the given IPv4 addresses. When no addresses are specified, nil is
+// returned.
+func ContainingIPv4Network(ips []net.IP) *net.IPNet {
+	if len(ips) == 0 {
+		return nil
+	}
+	network := net.IPNet{
+		IP:   ips[0],
+		Mask: net.CIDRMask(net.IPv4len*8, net.IPv4len*8),
+	}
+	for _, ip := range ips[1:] {
+		network.Mask = net.CIDRMask(commonPrefixLen(network.IP, ip), net.IPv4len*8)
+		network.IP = network.IP.Mask(network.Mask)
+	}
+	return &network
+}
+
+// commonPrefixLen reports the length of the longest prefix (looking
+// at the most significant, or leftmost, bits) that the
+// two addresses have in common, up to the length of a's prefix (i.e.,
+// the portion of the address not including the interface ID).
+//
+// If a or b is an IPv4 address as an IPv6 address, the IPv4 addresses
+// are compared (with max common prefix length of 32).
+// If a and b are different IP versions, 0 is returned.
+//
+// See https://tools.ietf.org/html/rfc6724#section-2.2
+//
+// copied from https://golang.org/pkg/net/?m=all#commonPrefixLen
+func commonPrefixLen(a, b net.IP) (cpl int) {
+	if a4 := a.To4(); a4 != nil {
+		a = a4
+	}
+	if b4 := b.To4(); b4 != nil {
+		b = b4
+	}
+	if len(a) != len(b) {
+		return 0
+	}
+	// If IPv6, only up to the prefix (first 64 bits)
+	if len(a) > 8 {
+		a = a[:8]
+		b = b[:8]
+	}
+	for len(a) > 0 {
+		if a[0] == b[0] {
+			cpl += 8
+			a = a[1:]
+			b = b[1:]
+			continue
+		}
+		bits := 8
+		ab, bb := a[0], b[0]
+		for {
+			ab >>= 1
+			bb >>= 1
+			bits--
+			if ab == bb {
+				cpl += bits
+				return
+			}
+		}
+	}
+	return
+}
diff --git a/report/networks_test.go b/report/networks_test.go
index 531a5ff0e3..59337f7b0d 100644
--- a/report/networks_test.go
+++ b/report/networks_test.go
@@ -4,6 +4,7 @@ import (
 	"net"
 	"testing"
 
+	"github.com/stretchr/testify/assert"
 	"github.com/weaveworks/scope/report"
 )
 
@@ -23,3 +24,18 @@ func TestContains(t *testing.T) {
 		t.Errorf("10.0.0.1 in %v", networks)
 	}
 }
+
+func TestContainingIPv4Network(t *testing.T) {
+	assert.Nil(t, containingIPv4Networks([]string{}))
+	assert.Equal(t, "10.0.0.1/32", containingIPv4Networks([]string{"10.0.0.1"}).String())
+	assert.Equal(t, "10.0.0.0/17", containingIPv4Networks([]string{"10.0.0.1", "10.0.2.55", "10.0.106.48"}).String())
+	assert.Equal(t, "0.0.0.0/0", containingIPv4Networks([]string{"10.0.0.1", "192.168.0.1"}).String())
+}
+
+func containingIPv4Networks(ipstrings []string) *net.IPNet {
+	ips := make([]net.IP, len(ipstrings))
+	for i, ip := range ipstrings {
+		ips[i] = net.ParseIP(ip)
+	}
+	return report.ContainingIPv4Network(ips)
+}