diff --git a/synapse/util/async_helpers.py b/synapse/util/async_helpers.py
index 080fc004036c..152ba40d8aea 100644
--- a/synapse/util/async_helpers.py
+++ b/synapse/util/async_helpers.py
@@ -550,16 +550,18 @@ def failure_cb(val):
     return new_d
 
 
+# This class can't be generic because it uses slots with attrs.
+# See: https://github.com/python-attrs/attrs/issues/313
 @attr.s(slots=True, frozen=True)
-class DoneAwaitable(Generic[R]):
+class DoneAwaitable:  # should be: Generic[R]
     """Simple awaitable that returns the provided value."""
 
-    value = attr.ib(type="R")
+    value = attr.ib(type=Any)  # should be: R
 
     def __await__(self):
         return self
 
-    def __iter__(self) -> "DoneAwaitable[R]":
+    def __iter__(self) -> "DoneAwaitable":
         return self
 
     def __next__(self) -> None:
diff --git a/synapse/util/caches/dictionary_cache.py b/synapse/util/caches/dictionary_cache.py
index 225591ca7ac6..ade088aae2ef 100644
--- a/synapse/util/caches/dictionary_cache.py
+++ b/synapse/util/caches/dictionary_cache.py
@@ -14,7 +14,7 @@
 import enum
 import logging
 import threading
-from typing import Dict, Generic, Iterable, Optional, Set, TypeVar
+from typing import Any, Dict, Generic, Iterable, Optional, Set, TypeVar
 
 import attr
 
@@ -31,8 +31,10 @@
 DV = TypeVar("DV")
 
 
+# This class can't be generic because it uses slots with attrs.
+# See: https://github.com/python-attrs/attrs/issues/313
 @attr.s(slots=True)
-class DictionaryEntry(Generic[DKT, DV]):
+class DictionaryEntry:  # should be: Generic[DKT, DV].
     """Returned when getting an entry from the cache
 
     Attributes:
@@ -45,8 +47,8 @@ class DictionaryEntry(Generic[DKT, DV]):
     """
 
     full = attr.ib(type=bool)
-    known_absent = attr.ib(type=Set[DKT])
-    value = attr.ib(type=Dict[DKT, DV])
+    known_absent = attr.ib(type=Set[Any])  # should be: Set[DKT]
+    value = attr.ib(type=Dict[Any, Any])  # should be: Dict[DKT, DV]
 
     def __len__(self) -> int:
         return len(self.value)
@@ -64,7 +66,7 @@ class DictionaryCache(Generic[KT, DKT, DV]):
     """
 
     def __init__(self, name: str, max_entries: int = 1000):
-        self.cache: LruCache[KT, DictionaryEntry[DKT, DV]] = LruCache(
+        self.cache: LruCache[KT, DictionaryEntry] = LruCache(
             max_size=max_entries, cache_name=name, size_callback=len
         )
 
@@ -84,7 +86,7 @@ def check_thread(self) -> None:
 
     def get(
         self, key: KT, dict_keys: Optional[Iterable[DKT]] = None
-    ) -> DictionaryEntry[DKT, DV]:
+    ) -> DictionaryEntry:
         """Fetch an entry out of the cache
 
         Args:
@@ -158,9 +160,7 @@ def _update_or_insert(
         # We pop and reinsert as we need to tell the cache the size may have
         # changed
 
-        entry: DictionaryEntry[DKT, DV] = self.cache.pop(
-            key, DictionaryEntry(False, set(), {})
-        )
+        entry: DictionaryEntry = self.cache.pop(key, DictionaryEntry(False, set(), {}))
         entry.value.update(value)
         entry.known_absent.update(known_absent)
         self.cache[key] = entry