diff --git a/service/debugger/debugger.go b/service/debugger/debugger.go
index 9da3e223..cab17bbb 100644
--- a/service/debugger/debugger.go
+++ b/service/debugger/debugger.go
@@ -1,6 +1,7 @@
 package debugger
 
 import (
+	"bytes"
 	"debug/dwarf"
 	"errors"
 	"fmt"
@@ -659,14 +660,51 @@ func (d *Debugger) ClearBreakpoint(requestedBp *api.Breakpoint) (*api.Breakpoint
 	d.processMutex.Lock()
 	defer d.processMutex.Unlock()
 
-	var clearedBp *api.Breakpoint
-	bp, err := d.target.ClearBreakpoint(requestedBp.Addr)
-	if err != nil {
-		return nil, fmt.Errorf("Can't clear breakpoint @%x: %s", requestedBp.Addr, err)
+	var bps []*proc.Breakpoint
+	var errs []error
+
+	clear := func(addr uint64) {
+		bp, err := d.target.ClearBreakpoint(addr)
+		if err != nil {
+			errs = append(errs, fmt.Errorf("address %#x: %v", addr, err))
+		}
+		if bp != nil {
+			bps = append(bps, bp)
+		}
+	}
+
+	clearAddr := true
+	for _, addr := range requestedBp.Addrs {
+		if addr == requestedBp.Addr {
+			clearAddr = false
+		}
+		clear(addr)
+	}
+	if clearAddr {
+		clear(requestedBp.Addr)
+	}
+
+	if len(errs) > 0 {
+		buf := new(bytes.Buffer)
+		for i, err := range errs {
+			fmt.Fprintf(buf, "%s", err)
+			if i != len(errs)-1 {
+				fmt.Fprintf(buf, ", ")
+			}
+		}
+
+		if len(bps) == 0 {
+			return nil, fmt.Errorf("unable to clear breakpoint %d: %v", requestedBp.ID, buf.String())
+		}
+		return nil, fmt.Errorf("unable to clear breakpoint %d (partial): %s", requestedBp.ID, buf.String())
+	}
+
+	clearedBp := api.ConvertBreakpoints(bps)
+	if len(clearedBp) < 0 {
+		return nil, nil
 	}
-	clearedBp = api.ConvertBreakpoint(bp)
 	d.log.Infof("cleared breakpoint: %#v", clearedBp)
-	return clearedBp, err
+	return clearedBp[0], nil
 }
 
 // Breakpoints returns the list of current breakpoints.
diff --git a/service/test/integration2_test.go b/service/test/integration2_test.go
index f05cbcc1..ee5bff81 100644
--- a/service/test/integration2_test.go
+++ b/service/test/integration2_test.go
@@ -52,20 +52,19 @@ func TestMain(m *testing.M) {
 }
 
 func withTestClient2(name string, t *testing.T, fn func(c service.Client)) {
-	withTestClient2Extended(name, t, func(c service.Client, fixture protest.Fixture) {
+	withTestClient2Extended(name, t, 0, func(c service.Client, fixture protest.Fixture) {
 		fn(c)
 	})
 }
 
-func startServer(name string, t *testing.T) (clientConn net.Conn, fixture protest.Fixture) {
+func startServer(name string, buildFlags protest.BuildFlags, t *testing.T) (clientConn net.Conn, fixture protest.Fixture) {
 	if testBackend == "rr" {
 		protest.MustHaveRecordingAllowed(t)
 	}
 	listener, clientConn := service.ListenerPipe()
 	defer listener.Close()
-	var buildFlags protest.BuildFlags
 	if buildMode == "pie" {
-		buildFlags = protest.BuildModePIE
+		buildFlags |= protest.BuildModePIE
 	}
 	fixture = protest.BuildFixture(name, buildFlags)
 	server := rpccommon.NewServer(&service.Config{
@@ -80,8 +79,8 @@ func startServer(name string, t *testing.T) (clientConn net.Conn, fixture protes
 	return clientConn, fixture
 }
 
-func withTestClient2Extended(name string, t *testing.T, fn func(c service.Client, fixture protest.Fixture)) {
-	clientConn, fixture := startServer(name, t)
+func withTestClient2Extended(name string, t *testing.T, buildFlags protest.BuildFlags, fn func(c service.Client, fixture protest.Fixture)) {
+	clientConn, fixture := startServer(name, buildFlags, t)
 	client := rpc2.NewClientFromConn(clientConn)
 	defer func() {
 		client.Detach(true)
@@ -697,7 +696,7 @@ func TestClientServer_FindLocations(t *testing.T) {
 		findLocationHelper(t, c, "main.stacktraceme", false, 1, stacktracemeAddr)
 	})
 
-	withTestClient2Extended("locationsUpperCase", t, func(c service.Client, fixture protest.Fixture) {
+	withTestClient2Extended("locationsUpperCase", t, 0, func(c service.Client, fixture protest.Fixture) {
 		// Upper case
 		findLocationHelper(t, c, "locationsUpperCase.go:6", false, 1, 0)
 
@@ -1765,7 +1764,7 @@ func (c *brokenRPCClient) call(method string, args, reply interface{}) error {
 }
 
 func TestUnknownMethodCall(t *testing.T) {
-	clientConn, _ := startServer("continuetestprog", t)
+	clientConn, _ := startServer("continuetestprog", 0, t)
 	client := &brokenRPCClient{jsonrpc.NewClient(clientConn)}
 	client.call("SetApiVersion", api.SetAPIVersionIn{APIVersion: 2}, &api.SetAPIVersionOut{})
 	defer client.Detach(true)
@@ -1904,3 +1903,27 @@ func TestStopRecording(t *testing.T) {
 		assertNoError(err, t, "GetState()")
 	})
 }
+
+func TestClearLogicalBreakpoint(t *testing.T) {
+	// Clearing a logical breakpoint should clear all associated physical
+	// breakpoints.
+	// Issue #1955.
+	withTestClient2Extended("testinline", t, protest.EnableInlining, func(c service.Client, fixture protest.Fixture) {
+		bp, err := c.CreateBreakpoint(&api.Breakpoint{FunctionName: "main.inlineThis"})
+		assertNoError(err, t, "CreateBreakpoint()")
+		t.Logf("breakpoint set at %#v", bp.Addrs)
+		if len(bp.Addrs) < 2 {
+			t.Fatal("Wrong number of addresses for main.inlineThis breakpoint")
+		}
+		_, err = c.ClearBreakpoint(bp.ID)
+		assertNoError(err, t, "ClearBreakpoint()")
+		bps, err := c.ListBreakpoints()
+		assertNoError(err, t, "ListBreakpoints()")
+		for _, curbp := range bps {
+			if curbp.ID == bp.ID {
+				t.Errorf("logical breakpoint still exists: %#v", curbp)
+				break
+			}
+		}
+	})
+}