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diff --git a/OPTIMIZATIONS b/OPTIMIZATIONS
index 3b6ebe1..6eed380 100644
--- a/OPTIMIZATIONS
+++ b/OPTIMIZATIONS
@@ -151,3 +151,29 @@ tests lowtag.
 FAST-+/FIXNUM and similar should accept unboxed arguments in interests
 of representation selection. Problem: inter-TN dependencies.
 --------------------------------------------------------------------------------
+#14
+The derived type of (/ (THE (DOUBLE-FLOAT (0D0)) X) (THE (DOUBLE-FLOAT
+1D0) Y)) is (DOUBLE-FLOAT 0.0d0). While it might be reasonable, it is
+better to derive (OR (MEMBER 0.0d0) (DOUBLE-FLOAT (0.0d0))).
+--------------------------------------------------------------------------------
+#15
+On the alpha, the system is reluctant to refer directly to a constant bignum,
+preferring to load a large constant through a slow sequence of instructions,
+then cons up a bignum for it:
+
+(LAMBDA (A)
+  (DECLARE (OPTIMIZE (SAFETY 1) (SPEED 3) (DEBUG 1))
+           (TYPE (INTEGER -10000 10000) A)
+           (IGNORABLE A))
+  (CASE A
+    ((89 125 16) (ASH A (MIN 18 -706)))
+    (T (DPB -3 (BYTE 30 30) -1))))
+--------------------------------------------------------------------------------
+#16
+(do ((i 0 (1+ i)))
+    ((= i (the (integer 0 100) n)))
+  ...)
+
+It is commonly expected for Python to derive (FIXNUMP I). (If ``='' is
+replaced with ``>='', Python will do.)
+--------------------------------------------------------------------------------