diff --git a/docs/release.rst b/docs/release.rst
index 93843513..68a751d3 100644
--- a/docs/release.rst
+++ b/docs/release.rst
@@ -16,6 +16,13 @@ Release notes
 Unreleased
 ----------
 
+Breaking changes
+~~~~~~~~~~~~~~~~
+* All arguments to the ``PCodec`` constructor except for ``level``
+  are now keyword only, to support the updated API.
+  By :user:`Sam Levang <slevang>`, :issue:`623`
+
+
 Fixes
 ~~~~~
 * Fixes issue with ``Delta`` Zarr 3 codec not working with ``astype``.
@@ -24,6 +31,10 @@ Fixes
 
 Improvements
 ~~~~~~~~~~~~
+* Add support for ``pcodec`` 0.3. This exposes the new ``delta_spec``
+  and ``paging_spec`` arguments, but maintains full backwards
+  compatibility for data written with older package versions.
+  By :user:`Sam Levang <slevang>`, :issue:`623`
 * If an import error is raised when trying to define a codec that is *not*
   an optional dependency, it is no longer silently caught. Instead it will
   be propagated to the user, as this indicates an issue with the installed
diff --git a/fixture/pcodec/codec.06/config.json b/fixture/pcodec/codec.06/config.json
new file mode 100644
index 00000000..982d0cc2
--- /dev/null
+++ b/fixture/pcodec/codec.06/config.json
@@ -0,0 +1,9 @@
+{
+    "delta_encoding_order": 2,
+    "delta_spec": "auto",
+    "equal_pages_up_to": 262144,
+    "id": "pcodec",
+    "level": 8,
+    "mode_spec": "auto",
+    "paging_spec": "equal_pages_up_to"
+}
\ No newline at end of file
diff --git a/fixture/pcodec/codec.06/encoded.00.dat b/fixture/pcodec/codec.06/encoded.00.dat
new file mode 100644
index 00000000..9332e78a
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diff --git a/fixture/pcodec/codec.06/encoded.01.dat b/fixture/pcodec/codec.06/encoded.01.dat
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index 00000000..e2729048
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diff --git a/fixture/pcodec/codec.06/encoded.02.dat b/fixture/pcodec/codec.06/encoded.02.dat
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diff --git a/fixture/pcodec/codec.06/encoded.03.dat b/fixture/pcodec/codec.06/encoded.03.dat
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diff --git a/fixture/pcodec/codec.06/encoded.05.dat b/fixture/pcodec/codec.06/encoded.05.dat
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index 00000000..6913bc0f
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diff --git a/fixture/pcodec/codec.06/encoded.06.dat b/fixture/pcodec/codec.06/encoded.06.dat
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index 00000000..a3fdce34
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diff --git a/fixture/pcodec/codec.06/encoded.07.dat b/fixture/pcodec/codec.06/encoded.07.dat
new file mode 100644
index 00000000..3498aaad
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diff --git a/fixture/pcodec/codec.06/encoded.08.dat b/fixture/pcodec/codec.06/encoded.08.dat
new file mode 100644
index 00000000..c5ab73c5
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diff --git a/fixture/pcodec/codec.06/encoded.09.dat b/fixture/pcodec/codec.06/encoded.09.dat
new file mode 100644
index 00000000..b8fe13fd
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diff --git a/fixture/pcodec/codec.07/config.json b/fixture/pcodec/codec.07/config.json
new file mode 100644
index 00000000..0dfb6337
--- /dev/null
+++ b/fixture/pcodec/codec.07/config.json
@@ -0,0 +1,9 @@
+{
+    "delta_encoding_order": null,
+    "delta_spec": "try_lookback",
+    "equal_pages_up_to": 262144,
+    "id": "pcodec",
+    "level": 8,
+    "mode_spec": "auto",
+    "paging_spec": "equal_pages_up_to"
+}
\ No newline at end of file
diff --git a/fixture/pcodec/codec.07/encoded.00.dat b/fixture/pcodec/codec.07/encoded.00.dat
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index 00000000..d7f0d767
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diff --git a/fixture/pcodec/codec.07/encoded.01.dat b/fixture/pcodec/codec.07/encoded.01.dat
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diff --git a/fixture/pcodec/codec.07/encoded.06.dat b/fixture/pcodec/codec.07/encoded.06.dat
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diff --git a/fixture/pcodec/codec.07/encoded.07.dat b/fixture/pcodec/codec.07/encoded.07.dat
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index 00000000..8c939467
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diff --git a/fixture/pcodec/codec.07/encoded.08.dat b/fixture/pcodec/codec.07/encoded.08.dat
new file mode 100644
index 00000000..e7057235
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diff --git a/fixture/pcodec/codec.07/encoded.09.dat b/fixture/pcodec/codec.07/encoded.09.dat
new file mode 100644
index 00000000..e0220dbf
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diff --git a/fixture/pcodec/codec.08/config.json b/fixture/pcodec/codec.08/config.json
new file mode 100644
index 00000000..b89edcab
--- /dev/null
+++ b/fixture/pcodec/codec.08/config.json
@@ -0,0 +1,9 @@
+{
+    "delta_encoding_order": null,
+    "delta_spec": "none",
+    "equal_pages_up_to": 262144,
+    "id": "pcodec",
+    "level": 8,
+    "mode_spec": "auto",
+    "paging_spec": "equal_pages_up_to"
+}
\ No newline at end of file
diff --git a/fixture/pcodec/codec.08/encoded.00.dat b/fixture/pcodec/codec.08/encoded.00.dat
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diff --git a/fixture/pcodec/codec.08/encoded.01.dat b/fixture/pcodec/codec.08/encoded.01.dat
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diff --git a/fixture/pcodec/codec.08/encoded.06.dat b/fixture/pcodec/codec.08/encoded.06.dat
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diff --git a/fixture/pcodec/codec.08/encoded.07.dat b/fixture/pcodec/codec.08/encoded.07.dat
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diff --git a/fixture/pcodec/codec.08/encoded.08.dat b/fixture/pcodec/codec.08/encoded.08.dat
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diff --git a/fixture/pcodec/codec.08/encoded.09.dat b/fixture/pcodec/codec.08/encoded.09.dat
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index 00000000..076ba5ad
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diff --git a/fixture/pcodec/codec.09/config.json b/fixture/pcodec/codec.09/config.json
new file mode 100644
index 00000000..39528178
--- /dev/null
+++ b/fixture/pcodec/codec.09/config.json
@@ -0,0 +1,9 @@
+{
+    "delta_encoding_order": 1,
+    "delta_spec": "try_consecutive",
+    "equal_pages_up_to": 262144,
+    "id": "pcodec",
+    "level": 8,
+    "mode_spec": "auto",
+    "paging_spec": "equal_pages_up_to"
+}
\ No newline at end of file
diff --git a/fixture/pcodec/codec.09/encoded.00.dat b/fixture/pcodec/codec.09/encoded.00.dat
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diff --git a/fixture/pcodec/codec.09/encoded.06.dat b/fixture/pcodec/codec.09/encoded.06.dat
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diff --git a/fixture/pcodec/codec.09/encoded.07.dat b/fixture/pcodec/codec.09/encoded.07.dat
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diff --git a/fixture/pcodec/codec.09/encoded.08.dat b/fixture/pcodec/codec.09/encoded.08.dat
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diff --git a/fixture/pcodec/codec.09/encoded.09.dat b/fixture/pcodec/codec.09/encoded.09.dat
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index 00000000..90d76bec
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diff --git a/numcodecs/pcodec.py b/numcodecs/pcodec.py
index ceb012f0..1739ff0b 100644
--- a/numcodecs/pcodec.py
+++ b/numcodecs/pcodec.py
@@ -4,7 +4,7 @@
 from numcodecs.compat import ensure_contiguous_ndarray
 
 try:
-    from pcodec import ChunkConfig, ModeSpec, PagingSpec, standalone
+    from pcodec import ChunkConfig, DeltaSpec, ModeSpec, PagingSpec, standalone
 except ImportError:  # pragma: no cover
     standalone = None
 
@@ -27,14 +27,21 @@ class PCodec(Codec):
     level : int
         A compression level from 0-12, where 12 take the longest and compresses
         the most.
-    delta_encoding_order : init or None
-        Either a delta encoding level from 0-7 or None. If set to None, pcodec
-        will try to infer the optimal delta encoding order.
-    mode_spec : {'auto', 'classic'}
+    mode_spec : {"auto", "classic"}
         Configures whether Pcodec should try to infer the best "mode" or
         structure of the data (e.g. approximate multiples of 0.1) to improve
         compression ratio, or skip this step and just use the numbers as-is
-        (Classic mode).
+        (Classic mode). Note that the "try*" specs are not currently supported.
+    delta_spec : {"auto", "none", "try_consecutive", "try_lookback"}
+        Configures the delta encoding strategy. By default, uses "auto" which
+        will try to infer the best encoding order.
+    paging_spec : {"equal_pages_up_to"}
+        Configures the paging strategy. Only "equal_pages_up_to" is currently
+        supported.
+    delta_encoding_order : int or None
+        Explicit delta encoding level from 0-7. Only valid if delta_spec is
+        "try_consecutive" or "auto" (to support backwards compatibility with
+        older versions of this codec).
     equal_pages_up_to : int
         Divide the chunk into equal pages of up to this many numbers.
     """
@@ -44,10 +51,12 @@ class PCodec(Codec):
     def __init__(
         self,
         level: int = 8,
+        *,
+        mode_spec: Literal["auto", "classic"] = "auto",
+        delta_spec: Literal["auto", "none", "try_consecutive", "try_lookback"] = "auto",
+        paging_spec: Literal["equal_pages_up_to"] = "equal_pages_up_to",
         delta_encoding_order: Optional[int] = None,
-        equal_pages_up_to: int = 262144,
-        # TODO one day, add support for the Try* mode specs
-        mode_spec: Literal['auto', 'classic'] = 'auto',
+        equal_pages_up_to: int = DEFAULT_MAX_PAGE_N,
     ):
         if standalone is None:  # pragma: no cover
             raise ImportError("pcodec must be installed to use the PCodec codec.")
@@ -55,28 +64,58 @@ def __init__(
         # note that we use `level` instead of `compression_level` to
         # match other codecs
         self.level = level
+        self.mode_spec = mode_spec
+        self.delta_spec = delta_spec
+        self.paging_spec = paging_spec
         self.delta_encoding_order = delta_encoding_order
         self.equal_pages_up_to = equal_pages_up_to
-        self.mode_spec = mode_spec
-
-    def encode(self, buf):
-        buf = ensure_contiguous_ndarray(buf)
 
+    def _get_chunk_config(self):
         match self.mode_spec:
-            case 'auto':
+            case "auto":
                 mode_spec = ModeSpec.auto()
-            case 'classic':
+            case "classic":
                 mode_spec = ModeSpec.classic()
             case _:
-                raise ValueError(f"unknown value for mode_spec: {self.mode_spec}")
-        paging_spec = PagingSpec.equal_pages_up_to(self.equal_pages_up_to)
+                raise ValueError(f"mode_spec {self.mode_spec} is not supported")
+
+        if self.delta_encoding_order is not None and self.delta_spec == "auto":
+            # backwards compat for before delta_spec was introduced
+            delta_spec = DeltaSpec.try_consecutive(self.delta_encoding_order)
+        elif self.delta_encoding_order is not None and self.delta_spec != "try_consecutive":
+            raise ValueError(
+                "delta_encoding_order can only be set for delta_spec='try_consecutive'"
+            )
+        else:
+            match self.delta_spec:
+                case "auto":
+                    delta_spec = DeltaSpec.auto()
+                case "none":
+                    delta_spec = DeltaSpec.none()
+                case "try_consecutive":
+                    delta_spec = DeltaSpec.try_consecutive(self.delta_encoding_order)
+                case "try_lookback":
+                    delta_spec = DeltaSpec.try_lookback()
+                case _:
+                    raise ValueError(f"delta_spec {self.delta_spec} is not supported")
+
+        match self.paging_spec:
+            case "equal_pages_up_to":
+                paging_spec = PagingSpec.equal_pages_up_to(self.equal_pages_up_to)
+            case _:
+                raise ValueError(f"paging_spec {self.paging_spec} is not supported")
 
         config = ChunkConfig(
             compression_level=self.level,
-            delta_encoding_order=self.delta_encoding_order,
+            delta_spec=delta_spec,
             mode_spec=mode_spec,
             paging_spec=paging_spec,
         )
+        return config
+
+    def encode(self, buf):
+        buf = ensure_contiguous_ndarray(buf)
+        config = self._get_chunk_config()
         return standalone.simple_compress(buf, config)
 
     def decode(self, buf, out=None):
diff --git a/numcodecs/tests/test_pcodec.py b/numcodecs/tests/test_pcodec.py
index c10549bd..63a2fb51 100644
--- a/numcodecs/tests/test_pcodec.py
+++ b/numcodecs/tests/test_pcodec.py
@@ -23,8 +23,12 @@
     PCodec(level=1),
     PCodec(level=5),
     PCodec(level=9),
-    PCodec(mode_spec='classic'),
+    PCodec(mode_spec="classic"),
     PCodec(equal_pages_up_to=300),
+    PCodec(delta_encoding_order=2),
+    PCodec(delta_spec="try_lookback"),
+    PCodec(delta_spec="none"),
+    PCodec(delta_spec="try_consecutive", delta_encoding_order=1),
 ]
 
 
@@ -56,15 +60,24 @@ def test_config():
     check_config(codec)
 
 
-def test_invalid_config_error():
-    codec = PCodec(mode_spec='bogus')
+@pytest.mark.parametrize("param", ["mode_spec", "delta_spec", "paging_spec"])
+def test_invalid_config_error(param):
+    codec = PCodec(**{param: "bogus"})
+    with pytest.raises(ValueError):
+        check_encode_decode_array_to_bytes(arrays[0], codec)
+
+
+def test_invalid_delta_encoding_combo():
+    codec = PCodec(delta_encoding_order=2, delta_spec="none")
     with pytest.raises(ValueError):
         check_encode_decode_array_to_bytes(arrays[0], codec)
 
 
 def test_repr():
     check_repr(
-        "PCodec(delta_encoding_order=None, equal_pages_up_to=262144, level=3, mode_spec='auto')"
+        "PCodec(delta_encoding_order=None, delta_spec='auto',"
+        " equal_pages_up_to=262144, level=3, mode_spec='auto',"
+        " paging_spec='equal_pages_up_to')"
     )
 
 
diff --git a/pyproject.toml b/pyproject.toml
index 928d901b..52ab34c3 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -67,7 +67,7 @@ zfpy = [
     "numpy<2.0.0",
 ]
 pcodec = [
-    "pcodec>=0.2,<0.3",
+    "pcodec>=0.3,<0.4",
 ]
 crc32c = [
     "crc32c>=2.7",