diff --git a/nibabel/_typing.py b/nibabel/_typing.py
new file mode 100644
index 000000000..8b6203181
--- /dev/null
+++ b/nibabel/_typing.py
@@ -0,0 +1,25 @@
+"""Helpers for typing compatibility across Python versions"""
+
+import sys
+
+if sys.version_info < (3, 10):
+    from typing_extensions import ParamSpec
+else:
+    from typing import ParamSpec
+
+if sys.version_info < (3, 11):
+    from typing_extensions import Self
+else:
+    from typing import Self
+
+if sys.version_info < (3, 13):
+    from typing_extensions import TypeVar
+else:
+    from typing import TypeVar
+
+
+__all__ = [
+    'ParamSpec',
+    'Self',
+    'TypeVar',
+]
diff --git a/nibabel/arrayproxy.py b/nibabel/arrayproxy.py
index ed2310519..82713f639 100644
--- a/nibabel/arrayproxy.py
+++ b/nibabel/arrayproxy.py
@@ -59,10 +59,11 @@
 
 if ty.TYPE_CHECKING:
     import numpy.typing as npt
-    from typing_extensions import Self  # PY310
+
+    from ._typing import Self, TypeVar
 
     # Taken from numpy/__init__.pyi
-    _DType = ty.TypeVar('_DType', bound=np.dtype[ty.Any])
+    _DType = TypeVar('_DType', bound=np.dtype[ty.Any])
 
 
 class ArrayLike(ty.Protocol):
diff --git a/nibabel/dataobj_images.py b/nibabel/dataobj_images.py
index 565a22879..3224376d4 100644
--- a/nibabel/dataobj_images.py
+++ b/nibabel/dataobj_images.py
@@ -20,12 +20,11 @@
 if ty.TYPE_CHECKING:
     import numpy.typing as npt
 
+    from ._typing import Self
     from .arrayproxy import ArrayLike
     from .fileholders import FileMap
     from .filename_parser import FileSpec
 
-ArrayImgT = ty.TypeVar('ArrayImgT', bound='DataobjImage')
-
 
 class DataobjImage(FileBasedImage):
     """Template class for images that have dataobj data stores"""
@@ -427,12 +426,12 @@ def ndim(self) -> int:
 
     @classmethod
     def from_file_map(
-        klass: type[ArrayImgT],
+        klass,
         file_map: FileMap,
         *,
         mmap: bool | ty.Literal['c', 'r'] = True,
         keep_file_open: bool | None = None,
-    ) -> ArrayImgT:
+    ) -> Self:
         """Class method to create image from mapping in ``file_map``
 
         Parameters
@@ -466,12 +465,12 @@ def from_file_map(
 
     @classmethod
     def from_filename(
-        klass: type[ArrayImgT],
+        klass,
         filename: FileSpec,
         *,
         mmap: bool | ty.Literal['c', 'r'] = True,
         keep_file_open: bool | None = None,
-    ) -> ArrayImgT:
+    ) -> Self:
         """Class method to create image from filename `filename`
 
         Parameters
diff --git a/nibabel/deprecated.py b/nibabel/deprecated.py
index d39c0624d..394fb0799 100644
--- a/nibabel/deprecated.py
+++ b/nibabel/deprecated.py
@@ -5,15 +5,11 @@
 import typing as ty
 import warnings
 
+from ._typing import ParamSpec
 from .deprecator import Deprecator
 from .pkg_info import cmp_pkg_version
 
-if ty.TYPE_CHECKING:
-    # PY39: ParamSpec is available in Python 3.10+
-    P = ty.ParamSpec('P')
-else:
-    # Just to keep the runtime happy
-    P = ty.TypeVar('P')
+P = ParamSpec('P')
 
 
 class ModuleProxy:
diff --git a/nibabel/filebasedimages.py b/nibabel/filebasedimages.py
index 086e31f12..853c39461 100644
--- a/nibabel/filebasedimages.py
+++ b/nibabel/filebasedimages.py
@@ -21,15 +21,11 @@
 from .openers import ImageOpener
 
 if ty.TYPE_CHECKING:
+    from ._typing import Self
     from .filename_parser import ExtensionSpec, FileSpec
 
 FileSniff = tuple[bytes, str]
 
-ImgT = ty.TypeVar('ImgT', bound='FileBasedImage')
-HdrT = ty.TypeVar('HdrT', bound='FileBasedHeader')
-
-StreamImgT = ty.TypeVar('StreamImgT', bound='SerializableImage')
-
 
 class ImageFileError(Exception):
     pass
@@ -39,7 +35,7 @@ class FileBasedHeader:
     """Template class to implement header protocol"""
 
     @classmethod
-    def from_header(klass: type[HdrT], header: FileBasedHeader | ty.Mapping | None = None) -> HdrT:
+    def from_header(klass, header: FileBasedHeader | ty.Mapping | None = None) -> Self:
         if header is None:
             return klass()
         # I can't do isinstance here because it is not necessarily true
@@ -53,7 +49,7 @@ def from_header(klass: type[HdrT], header: FileBasedHeader | ty.Mapping | None =
         )
 
     @classmethod
-    def from_fileobj(klass: type[HdrT], fileobj: io.IOBase) -> HdrT:
+    def from_fileobj(klass, fileobj: io.IOBase) -> Self:
         raise NotImplementedError
 
     def write_to(self, fileobj: io.IOBase) -> None:
@@ -65,7 +61,7 @@ def __eq__(self, other: object) -> bool:
     def __ne__(self, other: object) -> bool:
         return not self == other
 
-    def copy(self: HdrT) -> HdrT:
+    def copy(self) -> Self:
         """Copy object to independent representation
 
         The copy should not be affected by any changes to the original
@@ -245,12 +241,12 @@ def set_filename(self, filename: str) -> None:
         self.file_map = self.__class__.filespec_to_file_map(filename)
 
     @classmethod
-    def from_filename(klass: type[ImgT], filename: FileSpec) -> ImgT:
+    def from_filename(klass, filename: FileSpec) -> Self:
         file_map = klass.filespec_to_file_map(filename)
         return klass.from_file_map(file_map)
 
     @classmethod
-    def from_file_map(klass: type[ImgT], file_map: FileMap) -> ImgT:
+    def from_file_map(klass, file_map: FileMap) -> Self:
         raise NotImplementedError
 
     @classmethod
@@ -360,7 +356,7 @@ def instance_to_filename(klass, img: FileBasedImage, filename: FileSpec) -> None
         img.to_filename(filename)
 
     @classmethod
-    def from_image(klass: type[ImgT], img: FileBasedImage) -> ImgT:
+    def from_image(klass, img: FileBasedImage) -> Self:
         """Class method to create new instance of own class from `img`
 
         Parameters
@@ -540,7 +536,7 @@ def _filemap_from_iobase(klass, io_obj: io.IOBase) -> FileMap:
         return klass.make_file_map({klass.files_types[0][0]: io_obj})
 
     @classmethod
-    def from_stream(klass: type[StreamImgT], io_obj: io.IOBase) -> StreamImgT:
+    def from_stream(klass, io_obj: io.IOBase) -> Self:
         """Load image from readable IO stream
 
         Convert to BytesIO to enable seeking, if input stream is not seekable
@@ -567,7 +563,7 @@ def to_stream(self, io_obj: io.IOBase, **kwargs) -> None:
         self.to_file_map(self._filemap_from_iobase(io_obj), **kwargs)
 
     @classmethod
-    def from_bytes(klass: type[StreamImgT], bytestring: bytes) -> StreamImgT:
+    def from_bytes(klass, bytestring: bytes) -> Self:
         """Construct image from a byte string
 
         Class method
@@ -598,9 +594,7 @@ def to_bytes(self, **kwargs) -> bytes:
         return bio.getvalue()
 
     @classmethod
-    def from_url(
-        klass: type[StreamImgT], url: str | request.Request, timeout: float = 5
-    ) -> StreamImgT:
+    def from_url(klass, url: str | request.Request, timeout: float = 5) -> Self:
         """Retrieve and load an image from a URL
 
         Class method
diff --git a/nibabel/gifti/gifti.py b/nibabel/gifti/gifti.py
index 76fcc4a45..ff7a9bdde 100644
--- a/nibabel/gifti/gifti.py
+++ b/nibabel/gifti/gifti.py
@@ -867,7 +867,7 @@ def to_xml(self, enc='utf-8', *, mode='strict', **kwargs) -> bytes:
                 if arr.datatype not in GIFTI_DTYPES:
                     arr = copy(arr)
                     # TODO: Better typing for recoders
-                    dtype = cast(np.dtype, data_type_codes.dtype[arr.datatype])
+                    dtype = cast('np.dtype', data_type_codes.dtype[arr.datatype])
                     if np.issubdtype(dtype, np.floating):
                         arr.datatype = data_type_codes['float32']
                     elif np.issubdtype(dtype, np.integer):
diff --git a/nibabel/loadsave.py b/nibabel/loadsave.py
index e39aeceba..e398092ab 100644
--- a/nibabel/loadsave.py
+++ b/nibabel/loadsave.py
@@ -12,7 +12,6 @@
 from __future__ import annotations
 
 import os
-import typing as ty
 
 import numpy as np
 
@@ -26,13 +25,17 @@
 _compressed_suffixes = ('.gz', '.bz2', '.zst')
 
 
-if ty.TYPE_CHECKING:
+TYPE_CHECKING = False
+if TYPE_CHECKING:
+    from typing import TypedDict
+
+    from ._typing import ParamSpec
     from .filebasedimages import FileBasedImage
     from .filename_parser import FileSpec
 
-    P = ty.ParamSpec('P')
+    P = ParamSpec('P')
 
-    class Signature(ty.TypedDict):
+    class Signature(TypedDict):
         signature: bytes
         format_name: str
 
diff --git a/nibabel/nifti1.py b/nibabel/nifti1.py
index 5ea3041fc..e39f9f904 100644
--- a/nibabel/nifti1.py
+++ b/nibabel/nifti1.py
@@ -14,7 +14,6 @@
 from __future__ import annotations
 
 import json
-import sys
 import typing as ty
 import warnings
 from io import BytesIO
@@ -22,12 +21,8 @@
 import numpy as np
 import numpy.linalg as npl
 
-if sys.version_info < (3, 13):
-    from typing_extensions import Self, TypeVar  # PY312
-else:
-    from typing import Self, TypeVar
-
 from . import analyze  # module import
+from ._typing import Self, TypeVar
 from .arrayproxy import get_obj_dtype
 from .batteryrunners import Report
 from .casting import have_binary128
diff --git a/nibabel/openers.py b/nibabel/openers.py
index 35b10c20a..2d95d4813 100644
--- a/nibabel/openers.py
+++ b/nibabel/openers.py
@@ -22,7 +22,8 @@
     from types import TracebackType
 
     from _typeshed import WriteableBuffer
-    from typing_extensions import Self
+
+    from ._typing import Self
 
     ModeRT = ty.Literal['r', 'rt']
     ModeRB = ty.Literal['rb']
@@ -68,7 +69,7 @@ def __init__(
             if filename is None:
                 raise TypeError('Must define either fileobj or filename')
             # Cast because GzipFile.myfileobj has type io.FileIO while open returns ty.IO
-            fileobj = self.myfileobj = ty.cast(io.FileIO, open(filename, modestr))
+            fileobj = self.myfileobj = ty.cast('io.FileIO', open(filename, modestr))
         super().__init__(
             filename='',
             mode=modestr,
diff --git a/nibabel/pointset.py b/nibabel/pointset.py
index 759a0b15e..1d20b82fe 100644
--- a/nibabel/pointset.py
+++ b/nibabel/pointset.py
@@ -31,9 +31,9 @@
 from nibabel.spatialimages import SpatialImage
 
 if ty.TYPE_CHECKING:
-    from typing_extensions import Self
+    from ._typing import Self, TypeVar
 
-    _DType = ty.TypeVar('_DType', bound=np.dtype[ty.Any])
+    _DType = TypeVar('_DType', bound=np.dtype[ty.Any])
 
 
 class CoordinateArray(ty.Protocol):
diff --git a/nibabel/spatialimages.py b/nibabel/spatialimages.py
index a8e899359..bce17e734 100644
--- a/nibabel/spatialimages.py
+++ b/nibabel/spatialimages.py
@@ -138,6 +138,7 @@
 
 import numpy as np
 
+from ._typing import TypeVar
 from .casting import sctypes_aliases
 from .dataobj_images import DataobjImage
 from .filebasedimages import FileBasedHeader, FileBasedImage
@@ -152,11 +153,11 @@
 
     import numpy.typing as npt
 
+    from ._typing import Self
     from .arrayproxy import ArrayLike
     from .fileholders import FileMap
 
-SpatialImgT = ty.TypeVar('SpatialImgT', bound='SpatialImage')
-SpatialHdrT = ty.TypeVar('SpatialHdrT', bound='SpatialHeader')
+SpatialImgT = TypeVar('SpatialImgT', bound='SpatialImage')
 
 
 class HasDtype(ty.Protocol):
@@ -203,9 +204,9 @@ def __init__(
 
     @classmethod
     def from_header(
-        klass: type[SpatialHdrT],
+        klass,
         header: SpatialProtocol | FileBasedHeader | ty.Mapping | None = None,
-    ) -> SpatialHdrT:
+    ) -> Self:
         if header is None:
             return klass()
         # I can't do isinstance here because it is not necessarily true
@@ -227,7 +228,7 @@ def __eq__(self, other: object) -> bool:
             )
         return NotImplemented
 
-    def copy(self: SpatialHdrT) -> SpatialHdrT:
+    def copy(self) -> Self:
         """Copy object to independent representation
 
         The copy should not be affected by any changes to the original
@@ -586,7 +587,7 @@ def set_data_dtype(self, dtype: npt.DTypeLike) -> None:
         self._header.set_data_dtype(dtype)
 
     @classmethod
-    def from_image(klass: type[SpatialImgT], img: SpatialImage | FileBasedImage) -> SpatialImgT:
+    def from_image(klass, img: SpatialImage | FileBasedImage) -> Self:
         """Class method to create new instance of own class from `img`
 
         Parameters
@@ -610,7 +611,7 @@ def from_image(klass: type[SpatialImgT], img: SpatialImage | FileBasedImage) ->
         return super().from_image(img)
 
     @property
-    def slicer(self: SpatialImgT) -> SpatialFirstSlicer[SpatialImgT]:
+    def slicer(self) -> SpatialFirstSlicer[Self]:
         """Slicer object that returns cropped and subsampled images
 
         The image is resliced in the current orientation; no rotation or
@@ -658,7 +659,7 @@ def orthoview(self) -> OrthoSlicer3D:
         """
         return OrthoSlicer3D(self.dataobj, self.affine, title=self.get_filename())
 
-    def as_reoriented(self: SpatialImgT, ornt: Sequence[Sequence[int]]) -> SpatialImgT:
+    def as_reoriented(self, ornt: Sequence[Sequence[int]]) -> Self:
         """Apply an orientation change and return a new image
 
         If ornt is identity transform, return the original image, unchanged
diff --git a/nibabel/volumeutils.py b/nibabel/volumeutils.py
index cf23d905f..41bff7275 100644
--- a/nibabel/volumeutils.py
+++ b/nibabel/volumeutils.py
@@ -28,11 +28,13 @@
 
     import numpy.typing as npt
 
+    from ._typing import TypeVar
+
     Scalar = np.number | float
 
-    K = ty.TypeVar('K')
-    V = ty.TypeVar('V')
-    DT = ty.TypeVar('DT', bound=np.generic)
+    K = TypeVar('K')
+    V = TypeVar('V')
+    DT = TypeVar('DT', bound=np.generic)
 
 sys_is_le = sys.byteorder == 'little'
 native_code: ty.Literal['<', '>'] = '<' if sys_is_le else '>'
@@ -969,7 +971,7 @@ def working_type(
 
 
 def int_scinter_ftype(
-    ifmt: type[np.integer],
+    ifmt: np.dtype[np.integer] | type[np.integer],
     slope: npt.ArrayLike = 1.0,
     inter: npt.ArrayLike = 0.0,
     default: type[np.floating] = np.float32,
diff --git a/pyproject.toml b/pyproject.toml
index 73f01b66e..b6b420c79 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -11,7 +11,7 @@ readme = "README.rst"
 license = { text = "MIT License" }
 requires-python = ">=3.9"
 dependencies = [
-  "numpy >=1.22",
+  "numpy >=1.23",
   "packaging >=20",
   "importlib_resources >=5.12; python_version < '3.12'",
   "typing_extensions >=4.6; python_version < '3.13'",