diff --git a/spec.bs b/spec.bs
index 69c5ad9..b25552d 100644
--- a/spec.bs
+++ b/spec.bs
@@ -345,7 +345,7 @@ dictionary SubscribeOptions {
 };
 
 callback Predicate = boolean (any value, unsigned long long index);
-callback Reducer = any (any accumulator, any currentValue);
+callback Reducer = any (any accumulator, any currentValue, unsigned long long index);
 callback Mapper = any (any value, unsigned long long index);
 // Differs from Mapper only in return type, since this callback is exclusively
 // used to visit each element in a sequence, not transform it.
@@ -1604,7 +1604,67 @@ For now, see [https://github.com/wicg/observable#operators](https://github.com/w
   The <dfn for=Observable method><code>reduce(|reducer|, |initialValue|, |options|)</code></dfn>
   method steps are:
 
-    1. <span class=XXX>TODO: Spec this and use |reducer|, |initialValue|, and |options|.</span>
+    1. Let |p| [=a new promise=].
+
+    1. Let |controller| be a [=new=] {{AbortController}}.
+
+    1. Let |internal options| be a new {{SubscribeOptions}} whose {{SubscribeOptions/signal}} is the
+       result of [=creating a dependent abort signal=] from the list
+       «|controller|'s [=AbortController/signal=], |options|'s
+       {{SubscribeOptions/signal}} if non-null», using {{AbortSignal}}, and the [=current realm=].
+
+    1. If |internal options|'s {{SubscribeOptions/signal}} is [=AbortSignal/aborted=], then:
+
+       1. [=Reject=] |p| with |internal options|'s {{SubscribeOptions/signal}}'s
+          [=AbortSignal/abort reason=].
+
+       1. Return |p|.
+
+    1. [=AbortSignal/add|Add the following abort algorithm=] to |internal options|'s
+       {{SubscribeOptions/signal}}:
+
+       1. [=Reject=] |p| with |internal options|'s {{SubscribeOptions/signal}}'s [=AbortSignal/abort
+          reason=].
+
+    1. Let |idx| be an {{unsigned long long}}, initially 0.
+
+    1. Let |accumulator| be |initialValue| if it is given, and uninitialized otherwise.
+
+    1. Let |observer| be a new [=internal observer=], initialized as follows:
+
+       : [=internal observer/next steps=]
+       ::
+          1. If |accumulator| is uninitialized (meaning no |initialValue| was passed in), then set
+             |accumulator| to the passed in |value|, set |idx| to |idx| + 1, and abort these steps.
+
+             Note: This means that |reducer| will not be called with the first |value| that [=this=]
+             produces set as the {{Reducer/currentValue}}. Rather, when the *second* value is
+             eventually emitted, we will call |reducer| with *it* as the {{Reducer/currentValue}},
+             and the first value (that we're saving here) as the {{Reducer/accumulator}}.
+
+          1. [=Invoke=] |reducer| with |accumulator| as {{Reducer/accumulator}}, the passed in
+             |value| as {{Reducer/currentValue}}, and |idx| as {{Reducer/index}}. Let |result| be
+             the returned value.
+
+             If <a spec=webidl lt="an exception was thrown">an exception |E| was thrown</a>, then
+             [=reject=] |p| with |E|, and [=AbortController/signal abort=] |controller| with |E|.
+
+          1. Set |idx| to |idx| + 1.
+
+          1. Set |accumulator| to |result|.
+
+       : [=internal observer/error steps=]
+       :: [=Reject=] |p| with the passed in <var ignore>error</var>.
+
+       : [=internal observer/complete steps=]
+       :: 1. If |accumulator| is not "<code>unset</code>", then [=resolve=] |p| with |accumulator|.
+
+          Otherwise, [=reject=] |p| with a {{TypeError}}.
+
+    1. <a for=Observable lt="subscribe to an Observable">Subscribe</a> to [=this=] given |observer|
+       and |internal options|.
+
+    1. Return |p|.
 </div>