diff --git a/pkg/cmd/roachtest/election.go b/pkg/cmd/roachtest/election.go
index e243e89d1383..1d649371f96d 100644
--- a/pkg/cmd/roachtest/election.go
+++ b/pkg/cmd/roachtest/election.go
@@ -14,6 +14,7 @@ import (
 	"context"
 	"time"
 
+	"github.com/cockroachdb/cockroach/pkg/testutils/skip"
 	"github.com/cockroachdb/cockroach/pkg/util/timeutil"
 )
 
@@ -21,9 +22,10 @@ func registerElectionAfterRestart(r *testRegistry) {
 	r.Add(testSpec{
 		Name:    "election-after-restart",
 		Owner:   OwnerKV,
-		Skip:    "https://github.com/cockroachdb/cockroach/issues/35047",
 		Cluster: makeClusterSpec(3),
 		Run: func(ctx context.Context, t *test, c *cluster) {
+			skip.UnderRace(t, "race builds make this test exceed its timeout")
+
 			t.Status("starting up")
 			c.Put(ctx, cockroach, "./cockroach")
 			c.Start(ctx, t)
diff --git a/pkg/cmd/roachtest/kv.go b/pkg/cmd/roachtest/kv.go
index 3a50bd3a078b..3d756c9748e2 100644
--- a/pkg/cmd/roachtest/kv.go
+++ b/pkg/cmd/roachtest/kv.go
@@ -23,6 +23,7 @@ import (
 	"github.com/cockroachdb/cockroach/pkg/base"
 	"github.com/cockroachdb/cockroach/pkg/kv"
 	"github.com/cockroachdb/cockroach/pkg/sql/pgwire/pgerror"
+	"github.com/cockroachdb/cockroach/pkg/testutils/skip"
 	"github.com/cockroachdb/cockroach/pkg/ts/tspb"
 	"github.com/cockroachdb/cockroach/pkg/util/httputil"
 	"github.com/cockroachdb/cockroach/pkg/util/timeutil"
@@ -349,11 +350,12 @@ func registerKVQuiescenceDead(r *testRegistry) {
 
 func registerKVGracefulDraining(r *testRegistry) {
 	r.Add(testSpec{
-		Skip:    "https://github.com/cockroachdb/cockroach/issues/33501",
 		Name:    "kv/gracefuldraining/nodes=3",
 		Owner:   OwnerKV,
 		Cluster: makeClusterSpec(4),
 		Run: func(ctx context.Context, t *test, c *cluster) {
+			skip.UnderRace(t, "race builds make this test exceed its timeout")
+
 			nodes := c.spec.NodeCount - 1
 			c.Put(ctx, cockroach, "./cockroach", c.Range(1, nodes))
 			c.Put(ctx, workload, "./workload", c.Node(nodes+1))
diff --git a/pkg/cmd/roachtest/test.go b/pkg/cmd/roachtest/test.go
index 98e317b5bfe0..8e6992176172 100644
--- a/pkg/cmd/roachtest/test.go
+++ b/pkg/cmd/roachtest/test.go
@@ -21,6 +21,7 @@ import (
 	"strings"
 	"time"
 
+	"github.com/cockroachdb/cockroach/pkg/testutils/skip"
 	"github.com/cockroachdb/cockroach/pkg/util/syncutil"
 	"github.com/cockroachdb/cockroach/pkg/util/timeutil"
 	"github.com/cockroachdb/cockroach/pkg/util/version"
@@ -232,11 +233,24 @@ func (t *test) WorkerProgress(frac float64) {
 	t.progress(goid.Get(), frac)
 }
 
-// Skip records msg into t.spec.Skip and calls panic(errTestFatal) - thus
-// interrupting the running of the test.
-func (t *test) Skip(msg string, details string) {
-	t.spec.Skip = msg
-	t.spec.SkipDetails = details
+var _ skip.SkippableTest = (*test)(nil)
+
+// Skip skips the test. The first argument if any is the main message.
+// The remaining argument, if any, form the details.
+// This implements the skip.SkippableTest interface.
+func (t *test) Skip(args ...interface{}) {
+	if len(args) > 0 {
+		t.spec.Skip = fmt.Sprint(args[0])
+		args = args[1:]
+	}
+	t.spec.SkipDetails = fmt.Sprint(args...)
+	panic(errTestFatal)
+}
+
+// Skipf skips the test. The formatted message becomes the skip reason.
+// This implements the skip.SkippableTest interface.
+func (t *test) Skipf(format string, args ...interface{}) {
+	t.spec.Skip = fmt.Sprintf(format, args...)
 	panic(errTestFatal)
 }
 
diff --git a/pkg/testutils/skip/skip.go b/pkg/testutils/skip/skip.go
index 2d50520a5733..9f1648f4a1ac 100644
--- a/pkg/testutils/skip/skip.go
+++ b/pkg/testutils/skip/skip.go
@@ -17,8 +17,14 @@ import (
 	"github.com/cockroachdb/cockroach/pkg/util"
 )
 
+// SkippableTest is a testing.TB with Skip methods.
+type SkippableTest interface {
+	Skip(...interface{})
+	Skipf(string, ...interface{})
+}
+
 // WithIssue skips this test, logging the given issue ID as the reason.
-func WithIssue(t testing.TB, githubIssueID int, args ...interface{}) {
+func WithIssue(t SkippableTest, githubIssueID int, args ...interface{}) {
 	t.Skip(append([]interface{}{
 		fmt.Sprintf("https://github.com/cockroachdb/cockroach/issue/%d", githubIssueID)},
 		args...))
@@ -27,31 +33,31 @@ func WithIssue(t testing.TB, githubIssueID int, args ...interface{}) {
 // IgnoreLint skips this test, explicitly marking it as not a test that
 // should be tracked as a "skipped test" by external tools. You should use this
 // if, for example, your test should only be run in Race mode.
-func IgnoreLint(t testing.TB, args ...interface{}) {
+func IgnoreLint(t SkippableTest, args ...interface{}) {
 	t.Skip(args...)
 }
 
 // IgnoreLintf is like IgnoreLint, and it also takes a format string.
-func IgnoreLintf(t testing.TB, format string, args ...interface{}) {
+func IgnoreLintf(t SkippableTest, format string, args ...interface{}) {
 	t.Skipf(format, args...)
 }
 
 // UnderRace skips this test if the race detector is enabled.
-func UnderRace(t testing.TB, args ...interface{}) {
+func UnderRace(t SkippableTest, args ...interface{}) {
 	if util.RaceEnabled {
 		t.Skip(append([]interface{}{"disabled under race"}, args...))
 	}
 }
 
 // UnderShort skips this test if the -short flag is specified.
-func UnderShort(t testing.TB, args ...interface{}) {
+func UnderShort(t SkippableTest, args ...interface{}) {
 	if testing.Short() {
 		t.Skip(append([]interface{}{"disabled under -short"}, args...))
 	}
 }
 
 // UnderStress skips this test when running under stress.
-func UnderStress(t testing.TB, args ...interface{}) {
+func UnderStress(t SkippableTest, args ...interface{}) {
 	if NightlyStress() {
 		t.Skip(append([]interface{}{"disabled under stress"}, args...))
 	}
@@ -59,7 +65,7 @@ func UnderStress(t testing.TB, args ...interface{}) {
 
 // UnderStressRace skips this test during stressrace runs, which are tests
 // run under stress with the -race flag.
-func UnderStressRace(t testing.TB, args ...interface{}) {
+func UnderStressRace(t SkippableTest, args ...interface{}) {
 	if NightlyStress() && util.RaceEnabled {
 		t.Skip(append([]interface{}{"disabled under stressrace"}, args...))
 	}