diff --git a/cwltool/singularity.py b/cwltool/singularity.py
index 11380e3ed..3ed85c189 100644
--- a/cwltool/singularity.py
+++ b/cwltool/singularity.py
@@ -155,16 +155,67 @@ def is_version_3_10_or_newer() -> bool:
     return version >= Version("3.10")
 
 
+def _encode_container_image(string: str) -> str:
+    """
+    Produce a unique filename-safe string for a container image.
+
+    The input may be a Docker container specifier like "ubuntu",
+    "ubuntu:latest", "quay.io/adamnovak/hap.py:v0.3.15",
+    "quay.io/adamnovak/hap.py@sha256:f483da1b1c3d58be028a9599db4255cf1eb8570d50f901f10c8499fc36a94418",
+    etc., or it may be something with a protocol like "docker://ubuntu" or
+    "https://library.sylabs.io/v1/imagefile/library/default/alpine:latest", or
+    it may be a file path not ending in ":latest".
+
+    (It may not be a file path ending in ":latest" because it is too hard to
+    work out that the corresponding path without ":latest" should not have
+    ":latest" appended to it.)
+
+    If the input does not have a tag or digest, and a protocol was not used,
+    the "latest" tag will be used.
+
+    Distinct strings that refer to the same image (like "library/ubuntu",
+    "docker.io/library/ubuntu", and "docker://ubuntu:latest") will not
+    necessarily always produce the same result.
+
+    No two distinct inputs that refer to distinct container images will produce
+    the same result. The result is human-readable.
+    """
+    # See https://stackoverflow.com/a/43091578 for information on allowed
+    # patterns of Docker image specifiers.
+    has_tag_or_digest = re.search(
+        pattern=r"(:[a-zA-Z0-9_][a-zA-Z0-9._-]{0,127}|@[a-z0-9]+([+._-][a-z0-9]+)*:[a-zA-Z0-9=_-]+)$",
+        string=string,
+    )
+
+    has_protocol = re.search(pattern=r"^[a-zA-Z0-9-_]+://", string=string)
+
+    if not has_tag_or_digest and not has_protocol:
+        # We apply :latest to *everything* that doesn't seem to have a tag or a
+        # protocol
+        string += ":latest"
+
+    # First we need to escape existing underscores, and then we need to use
+    # underscore-based escapes to represent characters not allowed in
+    # filenames. There's sadly no one obvious way to do this.
+    return string.replace("_", "___").replace("/", "_s_")
+
+
 def _normalize_image_id(string: str) -> str:
-    if ":" not in string:
-        string += "_latest"
-    return string.replace("/", "_") + ".img"
+    return _encode_container_image(string) + ".img"
 
 
 def _normalize_sif_id(string: str) -> str:
-    if ":" not in string:
-        string += "_latest"
-    return string.replace("/", "_") + ".sif"
+    """
+    Produce a .sif filename for a container image.
+
+    This is guaranteed to be the same as the path at which cwl-docker-extract
+    from the cwl-utils project will save the .sif within its target directory,
+    for inputs supported by cwl-docker-extract.
+
+    When two inputs refer to different images, the results for those inputs are
+    guaranteed to be distinct.
+    """
+    return _encode_container_image(string) + ".sif"
 
 
 @mypyc_attr(allow_interpreted_subclasses=True)
diff --git a/tests/debian_image_id.cwl b/tests/debian_image_id.cwl
index 79ef9185b..9b2a7ece6 100755
--- a/tests/debian_image_id.cwl
+++ b/tests/debian_image_id.cwl
@@ -4,7 +4,7 @@ class: CommandLineTool
 
 requirements:
   DockerRequirement:
-    dockerImageId: 'debian:stable-slim.img'
+    dockerImageId: 'docker.io_s_debian:stable-slim.img'
 
 inputs:
   message: string
diff --git a/tests/debian_image_id2.cwl b/tests/debian_image_id2.cwl
index 5982a44c9..cbe90e8e7 100755
--- a/tests/debian_image_id2.cwl
+++ b/tests/debian_image_id2.cwl
@@ -4,7 +4,7 @@ class: CommandLineTool
 
 requirements:
   DockerRequirement:
-    dockerImageId: 'docker.io_debian:stable-slim.sif'
+    dockerImageId: 'docker.io_s_debian:stable-slim.sif'
 
 inputs:
   message: string
diff --git a/tests/test_singularity.py b/tests/test_singularity.py
index a6a1f7b4f..af66a4ddc 100644
--- a/tests/test_singularity.py
+++ b/tests/test_singularity.py
@@ -15,6 +15,7 @@
     _IMAGES,
     _IMAGES_LOCK,
     _inspect_singularity_sandbox_image,
+    _normalize_sif_id,
 )
 
 from .util import (
@@ -33,6 +34,47 @@ def clear_singularity_image_cache() -> None:
         _IMAGES.clear()
 
 
+def test_normalize_sif_id_resists_collision() -> None:
+    """Test that tricky image names can't collide."""
+    assert _normalize_sif_id("ubuntu:latest") != _normalize_sif_id("ubuntu_latest")
+    assert _normalize_sif_id("docker://user_name/repo") != _normalize_sif_id(
+        "docker://user/name_repo"
+    )
+    assert _normalize_sif_id("http://something.com/something.sif") != _normalize_sif_id(
+        "http:_something.com/something.sif"
+    )
+
+
+def test_normalize_sif_id_implies_latest() -> None:
+    """
+    Test that image names that imply latest are equivalent to those that
+    specify it.
+    """
+    assert _normalize_sif_id("ubuntu") == _normalize_sif_id("ubuntu:latest")
+    assert _normalize_sif_id("quay.io/adamnovak/hap.py") == _normalize_sif_id(
+        "quay.io/adamnovak/hap.py:latest"
+    )
+
+
+def test_normalize_sif_id_does_not_tag_protocols() -> None:
+    """
+    Test that if an image comes from a string with a protocol, no tag is added.
+    """
+    assert _normalize_sif_id("docker://library/ubuntu") != _normalize_sif_id(
+        "docker://library/ubuntu:latest"
+    )
+
+
+def test_normalize_sif_id_matches_cwl_utils_tests() -> None:
+    """
+    Make sure that the particular values tested in cwl-utils get the same
+    answers here as there.
+    """
+
+    assert _normalize_sif_id("some_name/repo:123") == "some___name_s_repo:123.sif"
+    assert _normalize_sif_id("some/name_repo:123") == "some_s_name___repo:123.sif"
+
+
 @needs_singularity_2_6
 def test_singularity_pullfolder(tmp_path: Path, monkeypatch: pytest.MonkeyPatch) -> None:
     """Test singularity respects SINGULARITY_PULLFOLDER."""
@@ -133,6 +175,10 @@ def test_singularity_local(tmp_path: Path) -> None:
 
 @needs_singularity_2_6
 def test_singularity2_docker_image_id_in_tool(tmp_path: Path) -> None:
+    """
+    Ensure that images end up cached at the expected path and are loadable from
+    it with Singularity 2.
+    """
     workdir = tmp_path / "working_dir"
     workdir.mkdir()
     with working_directory(workdir):
@@ -157,6 +203,10 @@ def test_singularity2_docker_image_id_in_tool(tmp_path: Path) -> None:
 
 @needs_singularity_3_or_newer
 def test_singularity3_docker_image_id_in_tool(tmp_path: Path) -> None:
+    """
+    Ensure that images end up cached at the expected path and are loadable from
+    it with Singularity 3.
+    """
     workdir = tmp_path / "working_dir"
     workdir.mkdir()
     with working_directory(workdir):
@@ -194,7 +244,7 @@ def test_singularity_dockerfile_no_name_no_cache(tmp_path: Path) -> None:
             ]
         )
         assert result_code == 0, stderr
-    assert not (workdir / "bea92b9b6910cbbd2ae602f5bb0f0f27_latest.sif").exists()
+    assert not (workdir / _normalize_sif_id("bea92b9b6910cbbd2ae602f5bb0f0f27")).exists()
 
 
 @needs_singularity_3_or_newer
@@ -217,8 +267,8 @@ def test_singularity_dockerfile_no_name_with_cache(
                 ]
             )
             assert result_code == 0, stderr
-    assert not (workdir / "bea92b9b6910cbbd2ae602f5bb0f0f27_latest.sif").exists()
-    assert (cachedir / "bea92b9b6910cbbd2ae602f5bb0f0f27_latest.sif").exists()
+    assert not (workdir / _normalize_sif_id("bea92b9b6910cbbd2ae602f5bb0f0f27")).exists()
+    assert (cachedir / _normalize_sif_id("bea92b9b6910cbbd2ae602f5bb0f0f27")).exists()
 
 
 @needs_singularity_3_or_newer
@@ -236,8 +286,8 @@ def test_singularity_dockerfile_with_name_no_cache(tmp_path: Path) -> None:
         )
         assert result_code == 0, stderr
     print(list(workdir.iterdir()))
-    assert not (workdir / "bea92b9b6910cbbd2ae602f5bb0f0f27_latest.sif").exists()
-    assert not (workdir / "customDebian_latest.sif").exists()
+    assert not (workdir / _normalize_sif_id("bea92b9b6910cbbd2ae602f5bb0f0f27")).exists()
+    assert not (workdir / _normalize_sif_id("customDebian")).exists()
 
 
 @needs_singularity_3_or_newer
@@ -262,10 +312,10 @@ def test_singularity_dockerfile_with_name_with_cache(
             print(list(workdir.iterdir()))
             print(list(cachedir.iterdir()))
             assert result_code == 0, stderr
-    assert not (workdir / "bea92b9b6910cbbd2ae602f5bb0f0f27_latest.sif").exists()
-    assert not (cachedir / "bea92b9b6910cbbd2ae602f5bb0f0f27_latest.sif").exists()
-    assert not (workdir / "customDebian_latest.sif").exists()
-    assert (cachedir / "customDebian_latest.sif").exists()
+    assert not (workdir / _normalize_sif_id("bea92b9b6910cbbd2ae602f5bb0f0f27")).exists()
+    assert not (cachedir / _normalize_sif_id("bea92b9b6910cbbd2ae602f5bb0f0f27")).exists()
+    assert not (workdir / _normalize_sif_id("customDebian")).exists()
+    assert (cachedir / _normalize_sif_id("customDebian")).exists()
 
 
 @needs_singularity