diff --git a/cli/clistat/cgroup.go b/cli/clistat/cgroup.go
index d4fc9976550ce..ffa2cf12b8afd 100644
--- a/cli/clistat/cgroup.go
+++ b/cli/clistat/cgroup.go
@@ -6,6 +6,7 @@ import (
 	"strconv"
 	"strings"
 
+	"github.com/hashicorp/go-multierror"
 	"github.com/spf13/afero"
 	"golang.org/x/xerrors"
 	"tailscale.com/types/ptr"
@@ -15,11 +16,10 @@ import (
 // Ref: https://www.kernel.org/doc/Documentation/cgroup-v1/cpuacct.txt
 const (
 	// CPU usage of all tasks in cgroup in nanoseconds.
-	cgroupV1CPUAcctUsage = "/sys/fs/cgroup/cpu/cpuacct.usage"
-	// Alternate path
-	cgroupV1CPUAcctUsageAlt = "/sys/fs/cgroup/cpu,cpuacct/cpuacct.usage"
+	cgroupV1CPUAcctUsage = "/sys/fs/cgroup/cpu,cpuacct/cpuacct.usage"
 	// CFS quota and period for cgroup in MICROseconds
-	cgroupV1CFSQuotaUs  = "/sys/fs/cgroup/cpu,cpuacct/cpu.cfs_quota_us"
+	cgroupV1CFSQuotaUs = "/sys/fs/cgroup/cpu,cpuacct/cpu.cfs_quota_us"
+	// CFS period for cgroup in MICROseconds
 	cgroupV1CFSPeriodUs = "/sys/fs/cgroup/cpu,cpuacct/cpu.cfs_period_us"
 	// Maximum memory usable by cgroup in bytes
 	cgroupV1MemoryMaxUsageBytes = "/sys/fs/cgroup/memory/memory.max_usage_in_bytes"
@@ -153,12 +153,26 @@ func (s *Statter) cGroupV2CPUTotal() (total float64, err error) {
 func (s *Statter) cGroupV1CPUTotal() (float64, error) {
 	periodUs, err := readInt64(s.fs, cgroupV1CFSPeriodUs)
 	if err != nil {
-		return 0, xerrors.Errorf("read cpu period: %w", err)
+		// Try alternate path under /sys/fs/cpu
+		var merr error
+		merr = multierror.Append(merr, xerrors.Errorf("get cpu period: %w", err))
+		periodUs, err = readInt64(s.fs, strings.Replace(cgroupV1CFSPeriodUs, "cpu,cpuacct", "cpu", 1))
+		if err != nil {
+			merr = multierror.Append(merr, xerrors.Errorf("get cpu period: %w", err))
+			return 0, merr
+		}
 	}
 
 	quotaUs, err := readInt64(s.fs, cgroupV1CFSQuotaUs)
 	if err != nil {
-		return 0, xerrors.Errorf("read cpu quota: %w", err)
+		// Try alternate path under /sys/fs/cpu
+		var merr error
+		merr = multierror.Append(merr, xerrors.Errorf("get cpu quota: %w", err))
+		quotaUs, err = readInt64(s.fs, strings.Replace(cgroupV1CFSQuotaUs, "cpu,cpuacct", "cpu", 1))
+		if err != nil {
+			merr = multierror.Append(merr, xerrors.Errorf("get cpu quota: %w", err))
+			return 0, merr
+		}
 	}
 
 	if quotaUs < 0 {
@@ -171,10 +185,13 @@ func (s *Statter) cGroupV1CPUTotal() (float64, error) {
 func (s *Statter) cGroupV1CPUUsed() (float64, error) {
 	usageNs, err := readInt64(s.fs, cgroupV1CPUAcctUsage)
 	if err != nil {
-		// try alternate path
-		usageNs, err = readInt64(s.fs, cgroupV1CPUAcctUsageAlt)
+		// Try alternate path under /sys/fs/cgroup/cpuacct
+		var merr error
+		merr = multierror.Append(merr, xerrors.Errorf("read cpu used: %w", err))
+		usageNs, err = readInt64(s.fs, strings.Replace(cgroupV1CPUAcctUsage, "cpu,cpuacct", "cpuacct", 1))
 		if err != nil {
-			return 0, xerrors.Errorf("read cpu used: %w", err)
+			merr = multierror.Append(merr, xerrors.Errorf("read cpu used: %w", err))
+			return 0, merr
 		}
 	}
 
@@ -182,7 +199,14 @@ func (s *Statter) cGroupV1CPUUsed() (float64, error) {
 	usageNs /= 1000
 	periodUs, err := readInt64(s.fs, cgroupV1CFSPeriodUs)
 	if err != nil {
-		return 0, xerrors.Errorf("get cpu period: %w", err)
+		// Try alternate path under /sys/fs/cpu
+		var merr error
+		merr = multierror.Append(merr, xerrors.Errorf("get cpu period: %w", err))
+		periodUs, err = readInt64(s.fs, strings.Replace(cgroupV1CFSPeriodUs, "cpu,cpuacct", "cpu", 1))
+		if err != nil {
+			merr = multierror.Append(merr, xerrors.Errorf("get cpu period: %w", err))
+			return 0, merr
+		}
 	}
 
 	return float64(usageNs) / float64(periodUs), nil
diff --git a/cli/clistat/stat_internal_test.go b/cli/clistat/stat_internal_test.go
index 25cb9e099f682..283c455129aa7 100644
--- a/cli/clistat/stat_internal_test.go
+++ b/cli/clistat/stat_internal_test.go
@@ -153,6 +153,24 @@ func TestStatter(t *testing.T) {
 			assert.Equal(t, "cores", cpu.Unit)
 		})
 
+		t.Run("ContainerCPU/AltPath", func(t *testing.T) {
+			t.Parallel()
+			fs := initFS(t, fsContainerCgroupV1AltPath)
+			fakeWait := func(time.Duration) {
+				// Fake 1 second in ns of usage
+				mungeFS(t, fs, "/sys/fs/cgroup/cpuacct/cpuacct.usage", "100000000")
+			}
+			s, err := New(WithFS(fs), withNproc(2), withWait(fakeWait))
+			require.NoError(t, err)
+			cpu, err := s.ContainerCPU()
+			require.NoError(t, err)
+			require.NotNil(t, cpu)
+			assert.Equal(t, 1.0, cpu.Used)
+			require.NotNil(t, cpu.Total)
+			assert.Equal(t, 2.5, *cpu.Total)
+			assert.Equal(t, "cores", cpu.Unit)
+		})
+
 		t.Run("ContainerMemory", func(t *testing.T) {
 			t.Parallel()
 			fs := initFS(t, fsContainerCgroupV1)
@@ -366,4 +384,15 @@ proc /proc/sys proc ro,nosuid,nodev,noexec,relatime 0 0`,
 		cgroupV1MemoryUsageBytes:    "536870912",
 		cgroupV1MemoryStat:          "total_inactive_file 268435456",
 	}
+	fsContainerCgroupV1AltPath = map[string]string{
+		procOneCgroup: "0::/docker/aa86ac98959eeedeae0ecb6e0c9ddd8ae8b97a9d0fdccccf7ea7a474f4e0bb1f",
+		procMounts: `overlay / overlay rw,relatime,lowerdir=/some/path:/some/path,upperdir=/some/path:/some/path,workdir=/some/path:/some/path 0 0
+proc /proc/sys proc ro,nosuid,nodev,noexec,relatime 0 0`,
+		"/sys/fs/cgroup/cpuacct/cpuacct.usage": "0",
+		"/sys/fs/cgroup/cpu/cpu.cfs_quota_us":  "250000",
+		"/sys/fs/cgroup/cpu/cpu.cfs_period_us": "100000",
+		cgroupV1MemoryMaxUsageBytes:            "1073741824",
+		cgroupV1MemoryUsageBytes:               "536870912",
+		cgroupV1MemoryStat:                     "total_inactive_file 268435456",
+	}
 )