diff --git a/pkg/coretag/coretag.go b/pkg/coretag/coretag.go
index 98e1485a97..9574b23617 100644
--- a/pkg/coretag/coretag.go
+++ b/pkg/coretag/coretag.go
@@ -41,6 +41,7 @@ func Enable() error {
 }
 
 // GetAllCoreTags returns the core tag of all the threads in the thread group.
+// PID 0 means the current pid.
 func GetAllCoreTags(pid int) ([]uint64, error) {
 	// prctl(PR_SCHED_CORE_GET, PR_SCHED_CORE_SCOPE_THREAD_GROUP, ...) is not supported
 	// in linux. So instead we get all threads from /proc/<pid>/task and get all the
@@ -75,9 +76,14 @@ func GetAllCoreTags(pid int) ([]uint64, error) {
 }
 
 // getTids returns set of tids as reported by /proc/<pid>/task.
+// PID 0 means the current PID.
 func getTids(pid int) (map[int]struct{}, error) {
 	tids := make(map[int]struct{})
-	files, err := os.ReadDir("/proc/" + strconv.Itoa(pid) + "/task")
+	path := "/proc/self/task"
+	if pid != 0 {
+		path = fmt.Sprintf("/proc/%d/task", pid)
+	}
+	files, err := os.ReadDir(path)
 	if err != nil {
 		return nil, err
 	}
diff --git a/pkg/coretag/coretag_test.go b/pkg/coretag/coretag_test.go
index 1930716c47..a9458499f2 100644
--- a/pkg/coretag/coretag_test.go
+++ b/pkg/coretag/coretag_test.go
@@ -16,6 +16,7 @@ package coretag
 
 import (
 	"os"
+	"reflect"
 	"testing"
 
 	"gvisor.dev/gvisor/pkg/hostos"
@@ -36,11 +37,19 @@ func TestEnable(t *testing.T) {
 		t.Fatalf("Enable() got error %v, wanted nil", err)
 	}
 
-	coreTags, err := GetAllCoreTags(os.Getpid())
+	pid := os.Getpid()
+	coreTags, err := GetAllCoreTags(pid)
 	if err != nil {
 		t.Fatalf("GetAllCoreTags() got error %v, wanted nil", err)
 	}
 	if len(coreTags) != 1 {
 		t.Fatalf("Got coreTags %v, wanted len(coreTags)=1", coreTags)
 	}
+	coreTagsSelf, err := GetAllCoreTags(0)
+	if err != nil {
+		t.Fatalf("GetAllCoreTags(0) got error %v, wanted nil", err)
+	}
+	if !reflect.DeepEqual(coreTags, coreTagsSelf) {
+		t.Fatalf("Got different coreTags for PID %d vs self: %v vs %v", pid, coreTags, coreTagsSelf)
+	}
 }
diff --git a/runsc/boot/loader_test.go b/runsc/boot/loader_test.go
index ab99ee5c2e..1fb54321a4 100644
--- a/runsc/boot/loader_test.go
+++ b/runsc/boot/loader_test.go
@@ -245,7 +245,7 @@ func TestStartSignal(t *testing.T) {
 func TestHostnetWithRawSockets(t *testing.T) {
 	// Drop CAP_NET_RAW from effective capabilities, if we have it.
 	pid := os.Getpid()
-	caps, err := capability.NewPid2(os.Getpid())
+	caps, err := capability.NewPid2(0)
 	if err != nil {
 		t.Fatalf("error getting capabilities for pid %d: %v", pid, err)
 	}
diff --git a/runsc/cmd/boot.go b/runsc/cmd/boot.go
index d736b80c51..4b0f3b188a 100644
--- a/runsc/cmd/boot.go
+++ b/runsc/cmd/boot.go
@@ -471,7 +471,7 @@ func (b *Boot) Execute(_ context.Context, f *flag.FlagSet, args ...any) subcomma
 
 		// Verify that all sentry threads are properly core tagged, and log
 		// current core tag.
-		coreTags, err := coretag.GetAllCoreTags(os.Getpid())
+		coreTags, err := coretag.GetAllCoreTags(0)
 		if err != nil {
 			util.Fatalf("Failed read current core tags: %v", err)
 		}
diff --git a/runsc/cmd/chroot.go b/runsc/cmd/chroot.go
index 00f0cf0a58..3de0b20125 100644
--- a/runsc/cmd/chroot.go
+++ b/runsc/cmd/chroot.go
@@ -82,6 +82,73 @@ func copyFile(dst, src string) error {
 	return err
 }
 
+// setupMinimalProcfs creates a minimal procfs-like tree at `${chroot}/proc`.
+func setupMinimalProcfs(chroot string) error {
+	// We can't always directly mount procfs because it may be obstructed
+	// by submounts within it. See https://gvisor.dev/issue/10944.
+	// All we really need from procfs is /proc/self and a few kernel
+	// parameter files, which are typically not obstructed.
+	// So we create a tmpfs at /proc and manually copy the kernel parameter
+	// files into it. Then, to get /proc/self, we mount either a new
+	// instance of procfs (if possible), or a recursive bind mount of the
+	// procfs we do have access to (which still contains the obstructed
+	// submounts but /proc/self is not obstructed), and we symlink
+	// our /proc/self to the one in that mount.
+	//
+	// Why not try to mount the new procfs instance at /proc directly?
+	// Because that would cause the set of files at /proc to differ
+	// between the "new procfs instance" case and the "recursive bind
+	// mount" case. Thus, this could introduce a bug whereby gVisor starts
+	// to depend on a /proc file that is present in one case but not the
+	// other, without decent test coverage to catch it.
+	procRoot := filepath.Join(chroot, "/proc")
+	if err := os.Mkdir(procRoot, 0755); err != nil {
+		return fmt.Errorf("error creating /proc in chroot: %v", err)
+	}
+	if err := specutils.SafeMount("runsc-proc", procRoot, "tmpfs",
+		unix.MS_NOSUID|unix.MS_NODEV|unix.MS_NOEXEC, "", "/proc"); err != nil {
+		return fmt.Errorf("error mounting tmpfs in /proc: %v", err)
+	}
+	flags := uint32(unix.MS_NOSUID | unix.MS_NODEV | unix.MS_NOEXEC | unix.MS_RDONLY)
+	procSubmountDir := "sandbox-proc"
+	if newProcfsErr := mountInChroot(chroot, "proc", "/proc/"+procSubmountDir, "proc", flags); newProcfsErr != nil {
+		log.Debugf("Unable to mount a new instance of the procfs file system at %q (%v); trying a recursive bind mount instead.", filepath.Join(procRoot, procSubmountDir), newProcfsErr)
+		procSubmountDir = "host-proc"
+		if bindErr := mountInChroot(chroot, "/proc", "/proc/"+procSubmountDir, "bind",
+			unix.MS_BIND|unix.MS_REC|flags); bindErr != nil {
+			return fmt.Errorf("error recursively bind-mounting proc at %q (%w) after also failing to mount a new procfs instance there (%v)", filepath.Join(procRoot, procSubmountDir), bindErr, newProcfsErr)
+		}
+		log.Debugf("Successfully mounted a recursive bind mount of procfs at %q; continuing.", filepath.Join(procRoot, procSubmountDir))
+	}
+	// Create needed directories.
+	for _, d := range []string{
+		"/proc/sys",
+		"/proc/sys/kernel",
+		"/proc/sys/vm",
+	} {
+		if err := os.Mkdir(filepath.Join(chroot, d), 0755); err != nil {
+			return fmt.Errorf("error creating directory %q: %v", filepath.Join(chroot, d), err)
+		}
+	}
+	// Copy needed files.
+	for _, f := range []string{
+		"/proc/sys/vm/mmap_min_addr",
+		"/proc/sys/kernel/cap_last_cap",
+	} {
+		if err := copyFile(filepath.Join(chroot, f), f); err != nil {
+			return fmt.Errorf("failed to copy %q -> %q: %w", f, filepath.Join(chroot, f), err)
+		}
+	}
+	// Create symlink for /proc/self.
+	if err := os.Symlink(procSubmountDir+"/self", filepath.Join(procRoot, "self")); err != nil {
+		return fmt.Errorf("error creating symlink %q -> %q: %w", filepath.Join(procRoot, "self"), procSubmountDir+"/self", err)
+	}
+	if err := os.Chmod(procRoot, 0o111); err != nil {
+		return fmt.Errorf("error chmodding %q: %v", procRoot, err)
+	}
+	return nil
+}
+
 // setUpChroot creates an empty directory with runsc mounted at /runsc and proc
 // mounted at /proc.
 func setUpChroot(spec *specs.Spec, conf *config.Config) error {
@@ -109,9 +176,8 @@ func setUpChroot(spec *specs.Spec, conf *config.Config) error {
 		log.Warningf("Failed to copy /etc/localtime: %v. UTC timezone will be used.", err)
 	}
 
-	flags := uint32(unix.MS_NOSUID | unix.MS_NODEV | unix.MS_NOEXEC | unix.MS_RDONLY)
-	if err := mountInChroot(chroot, "proc", "/proc", "proc", flags); err != nil {
-		return fmt.Errorf("error mounting proc in chroot: %v", err)
+	if err := setupMinimalProcfs(chroot); err != nil {
+		return fmt.Errorf("error setting up minimal procfs in chroot %q: %v", chroot, err)
 	}
 
 	if err := tpuProxyUpdateChroot("/", chroot, spec, conf); err != nil {
diff --git a/runsc/specutils/namespace.go b/runsc/specutils/namespace.go
index abbfa6350b..bd3754b08a 100644
--- a/runsc/specutils/namespace.go
+++ b/runsc/specutils/namespace.go
@@ -214,7 +214,7 @@ func SetUIDGIDMappings(cmd *exec.Cmd, s *specs.Spec) {
 
 // HasCapabilities returns true if the user has all capabilities in 'cs'.
 func HasCapabilities(cs ...capability.Cap) bool {
-	caps, err := capability.NewPid2(os.Getpid())
+	caps, err := capability.NewPid2(0)
 	if err != nil {
 		return false
 	}
diff --git a/test/e2e/runtime_in_docker_test.go b/test/e2e/runtime_in_docker_test.go
index 97c7e5aa96..9924c2c1d2 100644
--- a/test/e2e/runtime_in_docker_test.go
+++ b/test/e2e/runtime_in_docker_test.go
@@ -74,18 +74,6 @@ func (test testVariant) run(ctx context.Context, logger testutil.Logger, runscPa
 			ReadOnly: false,
 		})
 	}
-	// Mount an unobstructed view of procfs at /proc2 so that the runtime
-	// can mount a fresh procfs.
-	// TODO(gvisor.dev/issue/10944): Remove this once issue is fixed.
-	opts.Mounts = append(opts.Mounts, mount.Mount{
-		Type:     mount.TypeBind,
-		Source:   "/proc",
-		Target:   "/proc2",
-		ReadOnly: false,
-		BindOptions: &mount.BindOptions{
-			NonRecursive: true,
-		},
-	})
 	const wantMessage = "It became a jumble of words, a litany, almost a kind of glossolalia."
 	args := []string{
 		"/runtime",