diff --git a/index.bs b/index.bs
index 46c95ea..9d418a4 100644
--- a/index.bs
+++ b/index.bs
@@ -669,13 +669,12 @@ The <dfn method for=ModelContext>registerTool(<var>tool</var>, <var>options</var
 1. If |tool map|[|tool name|] [=map/exists=], then return [=a promise rejected with=] an
    {{InvalidStateError}} {{DOMException}}.
 
-1. If |tool name| or {{ModelContextTool/description}} is an empty string, then return [=a promise
-   rejected with=] an {{InvalidStateError}} {{DOMException}}.
+1. If |tool name| is not a non-empty string or |tool|'s {{ModelContextTool/description}} is the
+   empty string, then return [=a promise rejected with=] an {{InvalidStateError}} {{DOMException}}.
 
-1. If either |tool name| is the empty string, or its [=string/length=] is greater than 128, or if
-   |tool name| contains a [=code point=] that is not an [=ASCII alphanumeric=], U+005F (_),
-   U+002D (-), or U+002E (.), then return [=a promise rejected with=] an {{InvalidStateError}}
-   {{DOMException}}.
+1. If |tool name|'s [=string/length=] is greater than 128, or if |tool name| contains a [=code
+   point=] that is not an [=ASCII alphanumeric=], U+005F (_), U+002D (-), or U+002E (.), then
+   return [=a promise rejected with=] an {{InvalidStateError}} {{DOMException}}.
 
 1. Let |stringified input schema| be the empty string.
 
@@ -833,8 +832,8 @@ The <dfn method for=ModelContext>getTools(<var>options</var>)</dfn> method steps
 
       1. Let |callerOrigin| be |toolRequestor|'s [=Document/origin=].
 
-      1. If |toolOwnerIsRequested| be true if |targetOrigin| is [=same origin=] with |callerOrigin|,
-         or if |from origins| [=list/contains=] |targetOrigin|; otherwise, false.
+      1. Let |toolOwnerIsRequested| be true if |targetOrigin| is [=same origin=] with
+         |callerOrigin|, or if |from origins| [=list/contains=] |targetOrigin|; otherwise, false.
 
       1. If |toolOwnerIsRequested| is false, then [=iteration/continue=].