diff --git a/dev/util_gen_stub_file.py b/dev/util_gen_stub_file.py
index e405b119..92f43ee8 100644
--- a/dev/util_gen_stub_file.py
+++ b/dev/util_gen_stub_file.py
@@ -37,6 +37,8 @@
     "__next__",
 }
 skip = {
+    "__annotate_func__",
+    "__annotations_cache__",
     "__firstlineno__",
     "__static_attributes__",
     "__replace__",
diff --git a/doc/gates.md b/doc/gates.md
index 79bfed17..7f982502 100644
--- a/doc/gates.md
+++ b/doc/gates.md
@@ -4879,13 +4879,19 @@ detection event simulations and affect whether the observable is included in err
 makes it easier to benchmark all observables of a code, without having to introduce noiseless qubits entangled with the
 logical qubit to avoid the testing of the X observable anticommuting with the testing of the Z observable.
 
+Unlike a `DETECTOR` instruction which provides a complete description of a detector by listing all its constituent
+measurement records, an individual `OBSERVABLE_INCLUDE` instruction is not required to (and generally does not) fully
+describe a logical observable. Instead, measurement records or Pauli targets are added to it incrementally. A logical
+observable can be given both types of description: as a collection of Pauli targets and as a collection of measurement
+record targets.
+
 Parens Arguments:
 
     A non-negative integer specifying the index of the logical observable to add the measurement records to.
 
 Targets:
 
-    The measurement records to add to the specified observable.
+    The measurement records or Pauli terms to add to the specified observable.
 
 Example:
 
@@ -4921,6 +4927,12 @@ Example:
     OBSERVABLE_INCLUDE(0) X0 X1
     OBSERVABLE_INCLUDE(1) Z0 Z2
 
+    # Stim circuit may include a description of an observable in terms of Pauli targets
+    # alongside a description in terms of measurement records.
+    OBSERVABLE_INCLUDE(0) Z0 Z1
+    M 0 1
+    OBSERVABLE_INCLUDE(0) rec[-2] rec[-1]
+
 <a name="QUBIT_COORDS"></a>
 ### The 'QUBIT_COORDS' Instruction
 
diff --git a/src/stim/gates/gate_data_annotations.cc b/src/stim/gates/gate_data_annotations.cc
index ddf18f11..dbcaa62f 100644
--- a/src/stim/gates/gate_data_annotations.cc
+++ b/src/stim/gates/gate_data_annotations.cc
@@ -137,13 +137,19 @@ detection event simulations and affect whether the observable is included in err
 makes it easier to benchmark all observables of a code, without having to introduce noiseless qubits entangled with the
 logical qubit to avoid the testing of the X observable anticommuting with the testing of the Z observable.
 
+Unlike a `DETECTOR` instruction which provides a complete description of a detector by listing all its constituent
+measurement records, an individual `OBSERVABLE_INCLUDE` instruction is not required to (and generally does not) fully
+describe a logical observable. Instead, measurement records or Pauli targets are added to it incrementally. A logical
+observable can be given both types of description: as a collection of Pauli targets and as a collection of measurement
+record targets.
+
 Parens Arguments:
 
     A non-negative integer specifying the index of the logical observable to add the measurement records to.
 
 Targets:
 
-    The measurement records to add to the specified observable.
+    The measurement records or Pauli terms to add to the specified observable.
 
 Example:
 
@@ -178,6 +184,12 @@ Parens Arguments:
     DETECTOR rec[-3] rec[-6]
     OBSERVABLE_INCLUDE(0) X0 X1
     OBSERVABLE_INCLUDE(1) Z0 Z2
+
+    # Stim circuit may include a description of an observable in terms of Pauli targets
+    # alongside a description in terms of measurement records.
+    OBSERVABLE_INCLUDE(0) Z0 Z1
+    M 0 1
+    OBSERVABLE_INCLUDE(0) rec[-2] rec[-1]
 )MARKDOWN",
             .unitary_data = {},
             .flow_data = {},