diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 8b541ff50..c221a5fba 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -49,7 +49,7 @@ from eth2spec.utils.ssz.ssz_impl import (
     hash_tree_root,
     signing_root,
     serialize,
-    is_empty,
+    is_zero,
 )
 from eth2spec.utils.ssz.ssz_typing import (
     bit, boolean, Container, List, Vector, Bytes, uint64,
diff --git a/specs/core/1_custody-game.md b/specs/core/1_custody-game.md
index f79977442..63900681e 100644
--- a/specs/core/1_custody-game.md
+++ b/specs/core/1_custody-game.md
@@ -328,7 +328,7 @@ def get_reveal_period(state: BeaconState, validator_index: ValidatorIndex, epoch
 ```python
 def replace_empty_or_append(list: MutableSequence[Any], new_element: Any) -> int:
     for i in range(len(list)):
-        if is_empty(list[i]):
+        if is_zero(list[i]):
             list[i] = new_element
             return i
     list.append(new_element)
diff --git a/specs/simple-serialize.md b/specs/simple-serialize.md
index 802adc5a6..f479c5d00 100644
--- a/specs/simple-serialize.md
+++ b/specs/simple-serialize.md
@@ -14,7 +14,7 @@
         - [Variable-size and fixed-size](#variable-size-and-fixed-size)
         - [Aliases](#aliases)
         - [Default values](#default-values)
-            - [`is_empty`](#is_empty)
+            - [`is_zero`](#is_zero)
         - [Illegal types](#illegal-types)
     - [Serialization](#serialization)
         - [`uintN`](#uintn)
@@ -75,19 +75,21 @@ For convenience we alias:
 * `bit` to `boolean`
 * `byte` to `uint8` (this is a basic type)
 * `BytesN` to `Vector[byte, N]` (this is *not* a basic type)
-* `null`: `{}`, i.e. the empty container
+* `null`: `{}`
 
 ### Default values
 
 The default value of a type upon initialization is recursively defined using `0` for `uintN`, `False` for `boolean` and the elements of `Bitvector`, and `[]` for lists and `Bitlist`. Unions default to the first type in the union (with type index zero), which is `null` if present in the union.
 
-#### `is_empty`
+#### `is_zero`
 
-An SSZ object is called empty (and thus, `is_empty(object)` returns true) if it is equal to the default value for that type.
+An SSZ object is called zeroed (and thus, `is_zero(object)` returns true) if it is equal to the default value for that type.
 
 ### Illegal types
 
-Empty vector types (i.e. `[subtype, 0]` for some `subtype`) are not legal. The `null` type is only legal as the first type in a union subtype (i.e. with type index zero).
+- Empty vector types (`Vector[type, 0]`, `Bitvector[0]`) are illegal.
+- Containers with no fields are illegal.
+- The `null` type is only legal as the first type in a union subtype (i.e. with type index zero).
 
 ## Serialization
 
diff --git a/test_libs/pyspec/eth2spec/utils/ssz/ssz_impl.py b/test_libs/pyspec/eth2spec/utils/ssz/ssz_impl.py
index b005f2456..748386733 100644
--- a/test_libs/pyspec/eth2spec/utils/ssz/ssz_impl.py
+++ b/test_libs/pyspec/eth2spec/utils/ssz/ssz_impl.py
@@ -33,7 +33,7 @@ def deserialize_basic(value, typ: BasicType):
         raise Exception(f"Type not supported: {typ}")
 
 
-def is_empty(obj: SSZValue):
+def is_zero(obj: SSZValue):
     return type(obj).default() == obj