diff --git a/internal/cloudsql/instance.go b/internal/cloudsql/instance.go
index 57e05543..411a29c9 100644
--- a/internal/cloudsql/instance.go
+++ b/internal/cloudsql/instance.go
@@ -158,7 +158,11 @@ func (i *Instance) OpenConns() *uint64 {
 // Close closes the instance; it stops the refresh cycle and prevents it from
 // making additional calls to the Cloud SQL Admin API.
 func (i *Instance) Close() error {
+	i.mu.Lock()
+	defer i.mu.Unlock()
 	i.cancel()
+	i.cur.cancel()
+	i.next.cancel()
 	return nil
 }
 
@@ -254,6 +258,8 @@ func (i *Instance) refreshOperation(ctx context.Context) (*refreshOperation, err
 		err = cur.err
 	case <-ctx.Done():
 		err = ctx.Err()
+	case <-i.ctx.Done():
+		err = i.ctx.Err()
 	}
 	if err != nil {
 		return nil, err
@@ -285,6 +291,13 @@ func (i *Instance) scheduleRefresh(d time.Duration) *refreshOperation {
 	r := &refreshOperation{}
 	r.ready = make(chan struct{})
 	r.timer = time.AfterFunc(d, func() {
+		// instance has been closed, don't schedule anything
+		if err := i.ctx.Err(); err != nil {
+			r.err = err
+			close(r.ready)
+			return
+		}
+
 		ctx, cancel := context.WithTimeout(i.ctx, i.refreshTimeout)
 		defer cancel()
 
@@ -304,13 +317,6 @@ func (i *Instance) scheduleRefresh(d time.Duration) *refreshOperation {
 
 		close(r.ready)
 
-		select {
-		case <-i.ctx.Done():
-			// instance has been closed, don't schedule anything
-			return
-		default:
-		}
-
 		// Once the refresh is complete, update "current" with working
 		// refreshOperation and schedule a new refresh
 		i.mu.Lock()
diff --git a/internal/cloudsql/instance_test.go b/internal/cloudsql/instance_test.go
index 3665759b..a30da211 100644
--- a/internal/cloudsql/instance_test.go
+++ b/internal/cloudsql/instance_test.go
@@ -19,7 +19,6 @@ import (
 	"crypto/rand"
 	"crypto/rsa"
 	"errors"
-	"strings"
 	"testing"
 	"time"
 
@@ -223,7 +222,7 @@ func TestClose(t *testing.T) {
 	i.Close()
 
 	_, _, err = i.ConnectInfo(ctx, PublicIP)
-	if !strings.Contains(err.Error(), "context was canceled or expired") {
+	if !errors.Is(err, context.Canceled) {
 		t.Fatalf("failed to retrieve connect info: %v", err)
 	}
 }