diff --git a/_includes/cheatsheet-binary.md b/_includes/cheatsheet-binary.md
index f6ca30e..0acd577 100644
--- a/_includes/cheatsheet-binary.md
+++ b/_includes/cheatsheet-binary.md
@@ -5,8 +5,8 @@ For a value `V`, we write `«V»` for the binary encoding of `V`.
 
                          «#!V» = [0x86] ++ «V»
 
-      «V» if V ∈ Float         = [0x87] ++ varint(|binary32(V)|) ++ binary32(V)
-      «V» if V ∈ Double        = [0x87] ++ varint(|binary64(V)|) ++ binary64(V)
+      «V» if V ∈ Float         = [0x87, 0x04] ++ binary32(V)
+      «V» if V ∈ Double        = [0x87, 0x08] ++ binary64(V)
 
       «V» if V ∈ SignedInteger = [0xB0] ++ varint(|intbytes(V)|) ++ intbytes(V)
       «V» if V ∈ String        = [0xB1] ++ varint(|utf8(V)|) ++ utf8(V)
@@ -28,10 +28,10 @@ The functions `binary32(F)` and `binary64(D)` yield big-endian 4- and
 
 The function `intbytes(x)` is a big-endian two's-complement signed binary representation of
 `x`, taking exactly as many whole bytes as needed to unambiguously identify the value and its
-sign; in particular, `intbytes(0)` is the empty byte sequence.
+sign. In particular, `intbytes(0)` is the empty byte sequence.
 
-**Annotations.** To annotate an encoded value `«V»` (that *MUST NOT* itself already be
-annotated) with some sequence of `Value`s `V_1...V_m` (that *MUST* be non-empty),
+**Annotations.** To annotate an encoded value `«V»` (which *MUST NOT* itself already be
+annotated) with some sequence of `Value`s `V_1...V_m` (which *MUST* be non-empty),
 surround `«V»` as follows:
 
                «@V_1...@V_m V» = [0xBF] ++ «V» ++ «V_1» ++...++ «V_m» ++ [0x84]
diff --git a/preserves-binary.md b/preserves-binary.md
index f711078..f837b48 100644
--- a/preserves-binary.md
+++ b/preserves-binary.md
@@ -103,19 +103,7 @@ binary representation of `x`, taking exactly as many whole bytes as
 needed to unambiguously identify the value and its sign. The value 0
 needs zero bytes to identify the value; non-zero values need at least
 one byte, and the most-significant bit in the first byte is the sign
-bit. For example,
-
-      «-257» = B0 02 FE FF     «-2» = B0 01 FE       «255» = B0 02 00 FF
-      «-256» = B0 02 FF 00     «-1» = B0 01 FF       «256» = B0 02 01 00
-      «-255» = B0 02 FF 01      «0» = B0 00        «32767» = B0 02 7F FF
-      «-129» = B0 02 FF 7F      «1» = B0 01 01     «32768» = B0 03 00 80 00
-      «-128» = B0 01 80       «127» = B0 01 7F     «65535» = B0 03 00 FF FF
-      «-127» = B0 01 81       «128» = B0 02 00 80  «65536» = B0 03 01 00 00
-
-      «87112285931760246646623899502532662132736»
-        = B0 12 01 00 00 00 00 00 00 00
-                00 00 00 00 00 00 00 00
-                00 00
+bit. See the [examples in the appendix below](#signedinteger-examples).
 
 ### Strings, ByteStrings and Symbols.
 
@@ -195,16 +183,9 @@ a binary-syntax document; otherwise, it should be interpreted as text.
 
      80 - False
      81 - True
-    (82)  RESERVED
-    (83)  RESERVED
      84 - End marker
-    (85)  RESERVED
      86 - Embedded
      87 - Float and Double
-    (8x)  RESERVED 88-8F
-
-    (9x)  RESERVED
-    (Ax)  RESERVED
 
      B0 - Integer
      B1 - String
@@ -215,9 +196,12 @@ a binary-syntax document; otherwise, it should be interpreted as text.
      B6 - Set
      B7 - Dictionary
 
-    (Bx)  RESERVED B8-BE
      BF - Annotated Repr (not itself starting with BF) followed by annotations
 
+All tags fall in the range [`0x80`, `0xBF`].
+
+Tag values `82`, `83`, `85`, `88`...`AF`, and `B8`...`BE` are **reserved**.
+
 ## Appendix. Binary SignedInteger representation
 
 Languages that provide fixed-width machine word types may find the
@@ -236,5 +220,19 @@ values.
 | -2<sup>55</sup> ≤ n < 2<sup>55</sup> (i56) | 9              | `B0` `07` `XX` `XX` `XX` `XX` `XX` `XX` `XX`      |
 | -2<sup>63</sup> ≤ n < 2<sup>63</sup> (i64) | 10             | `B0` `08` `XX` `XX` `XX` `XX` `XX` `XX` `XX` `XX` |
 
+## <a id="signedinteger-examples"></a>Appendix. Binary SignedInteger examples
+
+      «-257» = B0 02 FE FF     «-2» = B0 01 FE       «255» = B0 02 00 FF
+      «-256» = B0 02 FF 00     «-1» = B0 01 FF       «256» = B0 02 01 00
+      «-255» = B0 02 FF 01      «0» = B0 00        «32767» = B0 02 7F FF
+      «-129» = B0 02 FF 7F      «1» = B0 01 01     «32768» = B0 03 00 80 00
+      «-128» = B0 01 80       «127» = B0 01 7F     «65535» = B0 03 00 FF FF
+      «-127» = B0 01 81       «128» = B0 02 00 80  «65536» = B0 03 01 00 00
+
+      «87112285931760246646623899502532662132736»
+        = B0 12 01 00 00 00 00 00 00 00
+                00 00 00 00 00 00 00 00
+                00 00
+
 <!-- Heading to visually offset the footnotes from the main document: -->
 ## Notes