diff --git a/libcontainer/cgroups/v1_utils.go b/libcontainer/cgroups/v1_utils.go
index f8487b0a..a94f2086 100644
--- a/libcontainer/cgroups/v1_utils.go
+++ b/libcontainer/cgroups/v1_utils.go
@@ -8,6 +8,10 @@ import (
 	"os"
 	"path/filepath"
 	"strings"
+	"syscall"
+
+	securejoin "github.com/cyphar/filepath-securejoin"
+	"golang.org/x/sys/unix"
 )
 
 // Code in this source file are specific to cgroup v1,
@@ -15,6 +19,7 @@ import (
 
 const (
 	CgroupNamePrefix = "name="
+	defaultPrefix    = "/sys/fs/cgroup"
 )
 
 var (
@@ -43,11 +48,59 @@ func IsNotFound(err error) bool {
 	return ok
 }
 
+func tryDefaultPath(cgroupPath, subsystem string) string {
+	if !strings.HasPrefix(defaultPrefix, cgroupPath) {
+		return ""
+	}
+
+	// remove possible prefix
+	subsystem = strings.TrimPrefix(subsystem, CgroupNamePrefix)
+
+	// Make sure we're still under defaultPrefix, and resolve
+	// a possible symlink (like cpu -> cpu,cpuacct).
+	path, err := securejoin.SecureJoin(defaultPrefix, subsystem)
+	if err != nil {
+		return ""
+	}
+
+	// (1) path should be a directory.
+	st, err := os.Lstat(path)
+	if err != nil || !st.IsDir() {
+		return ""
+	}
+
+	// (2) path should be a mount point.
+	pst, err := os.Lstat(filepath.Dir(path))
+	if err != nil {
+		return ""
+	}
+
+	if st.Sys().(*syscall.Stat_t).Dev == pst.Sys().(*syscall.Stat_t).Dev {
+		// parent dir has the same dev -- path is not a mount point
+		return ""
+	}
+
+	// (3) path should have 'cgroup' fs type.
+	fst := unix.Statfs_t{}
+	err = unix.Statfs(path, &fst)
+	if err != nil || fst.Type != unix.CGROUP_SUPER_MAGIC {
+		return ""
+	}
+
+	return path
+}
+
 // https://www.kernel.org/doc/Documentation/cgroup-v1/cgroups.txt
 func FindCgroupMountpoint(cgroupPath, subsystem string) (string, error) {
 	if IsCgroup2UnifiedMode() {
 		return "", errUnified
 	}
+
+	// Avoid parsing mountinfo by trying the default path first, if possible.
+	if path := tryDefaultPath(cgroupPath, subsystem); path != "" {
+		return path, nil
+	}
+
 	mnt, _, err := FindCgroupMountpointAndRoot(cgroupPath, subsystem)
 	return mnt, err
 }
@@ -57,9 +110,7 @@ func FindCgroupMountpointAndRoot(cgroupPath, subsystem string) (string, string,
 		return "", "", errUnified
 	}
 
-	// We are not using mount.GetMounts() because it's super-inefficient,
-	// parsing it directly sped up x10 times because of not using Sscanf.
-	// It was one of two major performance drawbacks in container start.
+	// Avoid parsing mountinfo by checking if subsystem is valid/available.
 	if !isSubsystemAvailable(subsystem) {
 		return "", "", NewNotFoundError(subsystem)
 	}