diff --git a/spec.html b/spec.html
index b644cd1..0044dd3 100644
--- a/spec.html
+++ b/spec.html
@@ -22,7 +22,6 @@ <h1>Uint8Array.prototype.toBase64 ( [ _options_ ] )</h1>
     1. Let _opts_ be ? GetOptionsObject(_options_).
     1. Let _alphabet_ be ? Get(_opts_, *"alphabet"*).
     1. If _alphabet_ is *undefined*, set _alphabet_ to *"base64"*.
-    1. If _alphabet_ is not a String, throw a *TypeError* exception.
     1. If _alphabet_ is neither *"base64"* nor *"base64url"*, throw a *TypeError* exception.
     1. Let _toEncode_ be ? GetUint8ArrayBytes(_O_).
     1. If _alphabet_ is *"base64"*, then
@@ -56,7 +55,6 @@ <h1>Uint8Array.fromBase64 ( _string_ [ , _options_ ] )</h1>
     1. Let _opts_ be ? GetOptionsObject(_options_).
     1. Let _alphabet_ be ? Get(_opts_, *"alphabet"*).
     1. If _alphabet_ is *undefined*, set _alphabet_ to *"base64"*.
-    1. If _alphabet_ is not a String, throw a *TypeError* exception.
     1. If _alphabet_ is neither *"base64"* nor *"base64url"*, throw a *TypeError* exception.
     1. Let _lastChunkHandling_ be ? Get(_opts_, *"lastChunkHandling"*).
     1. If _lastChunkHandling_ is *undefined*, set _lastChunkHandling_ to *"loose"*.
@@ -78,16 +76,14 @@ <h1>Uint8Array.prototype.setFromBase64 ( _string_ [ , _options_ ] )</h1>
     1. Let _opts_ be ? GetOptionsObject(_options_).
     1. Let _alphabet_ be ? Get(_opts_, *"alphabet"*).
     1. If _alphabet_ is *undefined*, set _alphabet_ to *"base64"*.
-    1. If _alphabet_ is not a String, throw a *TypeError* exception.
     1. If _alphabet_ is neither *"base64"* nor *"base64url"*, throw a *TypeError* exception.
     1. Let _lastChunkHandling_ be ? Get(_opts_, *"lastChunkHandling"*).
     1. If _lastChunkHandling_ is *undefined*, set _lastChunkHandling_ to *"loose"*.
     1. If _lastChunkHandling_ is not one of *"loose"*, *"strict"*, or *"stop-before-partial"*, throw a *TypeError* exception.
     1. Let _taRecord_ be MakeTypedArrayWithBufferWitnessRecord(_into_, ~seq-cst~).
     1. If IsTypedArrayOutOfBounds(_taRecord_) is *true*, throw a *TypeError* exception.
-    1. Let _byteLength_ be TypedArrayByteLength(_taRecord_).
-    1. Let _maxLength_ be _byteLength_.
-    1. Let _result_ be ? FromBase64(_string_, _alphabet_, _lastChunkHandling_, _maxLength_).
+    1. Let _byteLength_ be TypedArrayLength(_taRecord_).
+    1. Let _result_ be ? FromBase64(_string_, _alphabet_, _lastChunkHandling_, _byteLength_).
     1. Let _bytes_ be _result_.[[Bytes]].
     1. Let _written_ be the length of _bytes_.
     1. NOTE: FromBase64 does not invoke any user code, so the ArrayBuffer backing _into_ cannot have been detached or shrunk.
@@ -120,9 +116,8 @@ <h1>Uint8Array.prototype.setFromHex ( _string_ )</h1>
     1. If _string_ is not a String, throw a *TypeError* exception.
     1. Let _taRecord_ be MakeTypedArrayWithBufferWitnessRecord(_into_, ~seq-cst~).
     1. If IsTypedArrayOutOfBounds(_taRecord_) is *true*, throw a *TypeError* exception.
-    1. Let _byteLength_ be TypedArrayByteLength(_taRecord_).
-    1. Let _maxLength_ be _byteLength_.
-    1. Let _result_ be ? FromHex(_string_, _maxLength_).
+    1. Let _byteLength_ be TypedArrayLength(_taRecord_).
+    1. Let _result_ be ? FromHex(_string_, _byteLength_).
     1. Let _bytes_ be _result_.[[Bytes]].
     1. Let _written_ be the length of _bytes_.
     1. NOTE: FromHex does not invoke any user code, so the ArrayBuffer backing _into_ cannot have been detached or shrunk.
@@ -225,7 +220,7 @@ <h1>
     </h1>
     <dl class="header">
     </dl>
-    <p>The <dfn id="standard-base64-alphabet">standard base64 alphabet</dfn> is a List whose elements are the code points corresponding to every letter and number in the Unicode Basic Latin block along with *"+"* and *"/"*; that is, it is StringToCodePoints(*"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"*).</p>
+    <p>The <dfn id="standard-base64-alphabet">standard base64 alphabet</dfn> is the String whose elements are the code units corresponding to every letter and number in the Unicode Basic Latin block along with *"+"* and *"/"*; that is, it is *"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"*.</p>
     <emu-alg>
       1. Let _chunkLength_ be the length of _chunk_.
       1. If _chunkLength_ is 2, then
@@ -313,7 +308,7 @@ <h1>
           1. If _char_ is either *"+"* or *"/"*, throw a *SyntaxError* exception.
           1. Else if _char_ is *"-"*, set _char_ to *"+"*.
           1. Else if _char_ is *"_"*, set _char_ to *"/"*.
-        1. If _char_ is not an element of the standard base64 alphabet, throw a *SyntaxError* exception.
+        1. If the sole code unit of _char_ is not an element of the standard base64 alphabet, throw a *SyntaxError* exception.
         1. Let _remaining_ be _maxLength_ - the length of _bytes_.
         1. If _remaining_ = 1 and _chunkLength_ = 2, or if _remaining_ = 2 and _chunkLength_ = 3, then
           1. Return the Record { [[Read]]: _read_, [[Bytes]]: _bytes_ }.