diff --git a/overlord/hookstate/ctlcmd/is_connected.go b/overlord/hookstate/ctlcmd/is_connected.go
index 7cd30d04ea6..3bb8f8cdf0a 100644
--- a/overlord/hookstate/ctlcmd/is_connected.go
+++ b/overlord/hookstate/ctlcmd/is_connected.go
@@ -27,6 +27,7 @@ import (
 	"github.com/snapcore/snapd/overlord/ifacestate"
 	"github.com/snapcore/snapd/overlord/snapstate"
 	"github.com/snapcore/snapd/sandbox/cgroup"
+	"github.com/snapcore/snapd/snap"
 )
 
 var cgroupSnapNameFromPid = cgroup.SnapNameFromPid
@@ -37,7 +38,7 @@ type isConnectedCommand struct {
 	Positional struct {
 		PlugOrSlotSpec string `positional-args:"true" positional-arg-name:"<plug|slot>"`
 	} `positional-args:"true" required:"true"`
-	Pid int `long:"pid" description:"Process ID for a connected process"`
+	Pid int `long:"pid" description:"Process ID for a plausibly connected process"`
 }
 
 var shortIsConnectedHelp = i18n.G(`Return success if the given plug or slot is connected, and failure otherwise`)
@@ -51,6 +52,12 @@ $ echo $?
 
 Snaps can only query their own plugs and slots - snap name is implicit and
 implied by the snapctl execution context.
+
+The --pid option can be used to determine whether a plug or slot is
+connected to the snap identified by the given process ID.  In this
+mode, additional failure exit codes may be returned: 10 if the other
+process is not snap confined, or 11 if the other snap is not connected
+but uses classic confinement.
 `)
 
 func init() {
@@ -91,12 +98,16 @@ func (c *isConnectedCommand) Execute(args []string) error {
 		return fmt.Errorf("internal error: cannot get connections: %s", err)
 	}
 
-	var otherSnapName string
+	var otherSnap *snap.Info
 	if c.Pid != 0 {
-		otherSnapName, err = cgroupSnapNameFromPid(c.Pid)
-		// FIXME: should we treat non-snap processes as connected?
+		name, err := cgroupSnapNameFromPid(c.Pid)
+		if err != nil {
+			// Indicate that this pid is not a snap
+			return &UnsuccessfulError{ExitCode: 10}
+		}
+		otherSnap, err = snapstate.CurrentInfo(st, name)
 		if err != nil {
-			return fmt.Errorf("internal error: cannot get snap name for pid %d: %s", c.Pid, err)
+			return fmt.Errorf("internal error: cannot get snap info for pid %d: %s", c.Pid, err)
 		}
 	}
 
@@ -115,8 +126,8 @@ func (c *isConnectedCommand) Execute(args []string) error {
 
 		matchingPlug := connRef.PlugRef.Snap == snapName && connRef.PlugRef.Name == plugOrSlot
 		matchingSlot := connRef.SlotRef.Snap == snapName && connRef.SlotRef.Name == plugOrSlot
-		if otherSnapName != "" {
-			if matchingPlug && connRef.SlotRef.Snap == otherSnapName || matchingSlot && connRef.PlugRef.Snap == otherSnapName {
+		if otherSnap != nil {
+			if matchingPlug && connRef.SlotRef.Snap == otherSnap.InstanceName() || matchingSlot && connRef.PlugRef.Snap == otherSnap.InstanceName() {
 				return nil
 			}
 		} else {
@@ -126,5 +137,9 @@ func (c *isConnectedCommand) Execute(args []string) error {
 		}
 	}
 
+	if otherSnap != nil && otherSnap.Confinement == snap.ClassicConfinement {
+		return &UnsuccessfulError{ExitCode: 11}
+	}
+
 	return &UnsuccessfulError{ExitCode: 1}
 }
diff --git a/overlord/hookstate/ctlcmd/is_connected_test.go b/overlord/hookstate/ctlcmd/is_connected_test.go
index fc6f2b4b1f1..3cef152ca80 100644
--- a/overlord/hookstate/ctlcmd/is_connected_test.go
+++ b/overlord/hookstate/ctlcmd/is_connected_test.go
@@ -85,8 +85,12 @@ var isConnectedTests = []struct {
 	exitCode: 1,
 }, {
 	// snap1:plug1 is not connected to a non-snap pid
-	args: []string{"is-connected", "--pid", "42", "plug1"},
-	err:  "internal error: cannot get snap name for pid 42: Not a snap",
+	args:     []string{"is-connected", "--pid", "42", "plug1"},
+	exitCode: 10,
+}, {
+	// snap1:plug1 is not connected to snap4, but snap4 is classic
+	args:     []string{"is-connected", "--pid", "1004", "plug1"},
+	exitCode: 11,
 }, {
 	// snap1:slot1 is connected to snap3
 	args: []string{"is-connected", "--pid", "1003", "slot1"},
@@ -96,8 +100,12 @@ var isConnectedTests = []struct {
 	exitCode: 1,
 }, {
 	// snap1:slot1 is not connected to a non-snap pid
-	args: []string{"is-connected", "--pid", "42", "slot1"},
-	err:  "internal error: cannot get snap name for pid 42: Not a snap",
+	args:     []string{"is-connected", "--pid", "42", "slot1"},
+	exitCode: 10,
+}, {
+	// snap1:slot1 is not connected to snap4, but snap4 is classic
+	args:     []string{"is-connected", "--pid", "1004", "slot1"},
+	exitCode: 11,
 }}
 
 func mockInstalledSnap(c *C, st *state.State, snapYaml string) {
@@ -126,6 +134,22 @@ plugs:
     interface: x11
 slots:
   slot1:
+    interface: x11`)
+	mockInstalledSnap(c, s.st, `name: snap2
+slots:
+  slot2:
+    interface: x11`)
+	mockInstalledSnap(c, s.st, `name: snap3
+plugs:
+  plug4:
+    interface: x11
+slots:
+  slot3:
+    interface: x11`)
+	mockInstalledSnap(c, s.st, `name: snap4
+confinement: classic
+slots:
+  slot4:
     interface: x11`)
 	restore := ctlcmd.MockCgroupSnapNameFromPid(func(pid int) (string, error) {
 		switch {