diff --git a/swh/model/identifiers.py b/swh/model/identifiers.py
--- a/swh/model/identifiers.py
+++ b/swh/model/identifiers.py
@@ -10,7 +10,6 @@
 from typing import Any, Dict, Union
 
 import attr
-from deprecated import deprecated
 
 from .collections import ImmutableDict
 from .exceptions import ValidationError
@@ -30,13 +29,6 @@
 SWHID_SEP = ":"
 SWHID_CTXT_SEP = ";"
 
-# deprecated variables
-PID_NAMESPACE = SWHID_NAMESPACE
-PID_VERSION = SWHID_VERSION
-PID_TYPES = SWHID_TYPES
-PID_SEP = SWHID_SEP
-PID_CTXT_SEP = SWHID_CTXT_SEP
-
 
 @lru_cache()
 def identifier_to_bytes(identifier):
@@ -736,20 +728,6 @@
         return swhid
 
 
-@deprecated("Use swh.model.identifiers.SWHID instead")
-class PersistentId(SWHID):
-    """
-    Named tuple holding the relevant info associated to a SoftWare Heritage
-    persistent IDentifier.
-
-    .. deprecated:: 0.3.8
-        Use :class:`swh.model.identifiers.SWHID` instead
-
-    """
-
-    pass
-
-
 def swhid(
     object_type: str,
     object_id: Union[str, Dict[str, Any]],
@@ -784,17 +762,6 @@
     return str(swhid)
 
 
-@deprecated("Use swh.model.identifiers.swhid instead")
-def persistent_identifier(*args, **kwargs) -> str:
-    """Compute :ref:`persistent-identifiers`
-
-    .. deprecated:: 0.3.8
-        Use :func:`swh.model.identifiers.swhid` instead
-
-    """
-    return swhid(*args, **kwargs)
-
-
 def parse_swhid(swhid: str) -> SWHID:
     """Parse :ref:`persistent-identifiers`.
 
@@ -848,13 +815,3 @@
         _id,
         _metadata,  # type: ignore  # mypy can't properly unify types
     )
-
-
-@deprecated("Use swh.model.identifiers.parse_swhid instead")
-def parse_persistent_identifier(persistent_id: str) -> PersistentId:
-    """Parse :ref:`persistent-identifiers`.
-
-    .. deprecated:: 0.3.8
-        Use :func:`swh.model.identifiers.parse_swhid` instead
-    """
-    return PersistentId(**parse_swhid(persistent_id).to_dict())
diff --git a/swh/model/model.py b/swh/model/model.py
--- a/swh/model/model.py
+++ b/swh/model/model.py
@@ -856,7 +856,7 @@
                     "Got SWHID as id for origin metadata (expected an URL)."
                 )
         else:
-            self._check_pid(self.type.value, value)
+            self._check_swhid(self.type.value, value)
 
     @discovery_date.validator
     def check_discovery_date(self, attribute, value):
@@ -925,7 +925,7 @@
                 f"Unexpected 'snapshot' context for {self.type.value} object: {value}"
             )
 
-        self._check_pid("snapshot", value)
+        self._check_swhid("snapshot", value)
 
     @release.validator
     def check_release(self, attribute, value):
@@ -941,7 +941,7 @@
                 f"Unexpected 'release' context for {self.type.value} object: {value}"
             )
 
-        self._check_pid("release", value)
+        self._check_swhid("release", value)
 
     @revision.validator
     def check_revision(self, attribute, value):
@@ -953,7 +953,7 @@
                 f"Unexpected 'revision' context for {self.type.value} object: {value}"
             )
 
-        self._check_pid("revision", value)
+        self._check_swhid("revision", value)
 
     @path.validator
     def check_path(self, attribute, value):
@@ -975,20 +975,20 @@
                 f"Unexpected 'directory' context for {self.type.value} object: {value}"
             )
 
-        self._check_pid("directory", value)
+        self._check_swhid("directory", value)
 
-    def _check_pid(self, expected_object_type, pid):
-        if isinstance(pid, str):
-            raise ValueError(f"Expected SWHID, got a string: {pid}")
+    def _check_swhid(self, expected_object_type, swhid):
+        if isinstance(swhid, str):
+            raise ValueError(f"Expected SWHID, got a string: {swhid}")
 
-        if pid.object_type != expected_object_type:
+        if swhid.object_type != expected_object_type:
             raise ValueError(
                 f"Expected SWHID type '{expected_object_type}', "
-                f"got '{pid.object_type}' in {pid}"
+                f"got '{swhid.object_type}' in {swhid}"
             )
 
-        if pid.metadata:
-            raise ValueError(f"Expected core SWHID, but got: {pid}")
+        if swhid.metadata:
+            raise ValueError(f"Expected core SWHID, but got: {swhid}")
 
     def to_dict(self):
         d = super().to_dict()