diff --git a/spec/API_specification/function_and_method_signatures.md b/spec/API_specification/function_and_method_signatures.rst
similarity index 52%
rename from spec/API_specification/function_and_method_signatures.md
rename to spec/API_specification/function_and_method_signatures.rst
index d199bcbb6..86d0819a6 100644
--- a/spec/API_specification/function_and_method_signatures.md
+++ b/spec/API_specification/function_and_method_signatures.rst
@@ -1,36 +1,34 @@
-(function-and-method-signatures)=
+.. _function-and-method-signatures:
 
-# Function and method signatures
+Function and method signatures
+==============================
 
 Function signatures in this standard adhere to the following:
 
-1. Positional parameters must be
-   [positional-only](https://www.python.org/dev/peps/pep-0570/) parameters.
+1. Positional parameters must be `positional-only <https://www.python.org/dev/peps/pep-0570/>`_ parameters.
    Positional-only parameters have no externally-usable name. When a function
    accepting positional-only parameters is called, positional arguments are
    mapped to these parameters based solely on their order.
 
-   _Rationale: existing libraries have incompatible conventions, and using names
-   of positional parameters is not normal/recommended practice._
+   *Rationale: existing libraries have incompatible conventions, and using names
+   of positional parameters is not normal/recommended practice.*
 
-    ```{note}
+   .. note::
 
     Positional-only parameters are only available in Python >= 3.8. Libraries
     still supporting 3.7 or 3.6 may consider making the API standard-compliant
     namespace >= 3.8. Alternatively, they can add guidance to their users in the
-    documentation to use the functions as if they were positional-only. 
-    ```
+    documentation to use the functions as if they were positional-only.
 
-2. Optional parameters must be
-   [keyword-only](https://www.python.org/dev/peps/pep-3102/) arguments.
+2. Optional parameters must be `keyword-only <https://www.python.org/dev/peps/pep-3102/>`_ arguments.
 
-   _Rationale: this leads to more readable code, and it makes it easier to
+   *Rationale: this leads to more readable code, and it makes it easier to
    evolve an API over time by adding keywords without having to worry about
-   keyword order._
+   keyword order.*
 
 3. For functions that have a single positional array parameter, that parameter
-   is called `x`. For functions that have multiple array parameters, those
-   parameters are called `xi` with `i = 1, 2, ...` (i.e., `x1`, `x2`).
+   is called ``x``. For functions that have multiple array parameters, those
+   parameters are called ``xi`` with ``i = 1, 2, ...`` (i.e., ``x1``, ``x2``).
 
 4. Type annotations are left out of the signatures themselves for readability; however,
    they are added to individual parameter descriptions. For code which aims to
@@ -38,25 +36,24 @@ Function signatures in this standard adhere to the following:
 
 A function signature and description will look like:
 
-```
-funcname(x1, x2, /, *, key1=-1, key2=None)
+::
 
-    Parameters
+   funcname(x1, x2, /, *, key1=-1, key2=None) -> out:
+       Parameters
 
-    x1 : array
-        description
-    x2 : array
-        description
-    key1 : int
-        description
-    key2 : Optional[str]
-        description
+        x1 : array
+            description
+        x2 : array
+            description
+        key1 : int
+            description
+        key2 : Optional[str]
+            description
 
-    Returns
+        Returns
 
-    out : array
-        description
-```
+        out : array
+            description
 
-Method signatures will follow the same conventions modulo the addition of
-`self`.
+
+Method signatures will follow the same conventions modulo the addition of ``self``.