diff --git a/unicodetools/src/main/resources/org/unicode/text/UCD/UnicodeInvariantTest.txt b/unicodetools/src/main/resources/org/unicode/text/UCD/UnicodeInvariantTest.txt
index 69e23177d..485a35d5d 100644
--- a/unicodetools/src/main/resources/org/unicode/text/UCD/UnicodeInvariantTest.txt
+++ b/unicodetools/src/main/resources/org/unicode/text/UCD/UnicodeInvariantTest.txt
@@ -586,12 +586,22 @@ Let $nonAlphabeticAvagrahas = [\N{TIBETAN MARK PALUTA}]  # A punctuation mark.
 [\p{InSC=Avagraha} - $nonAlphabeticAvagrahas] ⊆ \p{Alphabetic}
 
 # Name-based checks.
+Let $nonLowercaseSmallLetters = [ \p{name=/^LIMBU SMALL LETTER/} \N{TURNED GREEK SMALL LETTER IOTA} \p{name=/^(SQUARED|PARENTHESIZED|TAG) LATIN SMALL LETTER/} ]
+Let $nonLowercaseSmallModifierLetters = [ \p{gc=Lm} & \p{name=/^ARABIC SMALL/} ]
+[ \p{name=/\bSMALL LETTER\b/}-\p{gc=Mn}-\p{gc=Lt} - $nonLowercaseSmallLetters ] ⊆ \p{Lowercase}
+[ [\p{gc=Lm} & \p{name=/SMALL/}] - $nonLowercaseSmallModifierLetters ] ⊆ \p{Lowercase}
 
 # Combining letters are often alphabetic (medievalist abbreviations).
 # The others are diacritic (cantillation marks, phonetics).
 # See 177-C52.
 \p{name=/COMBINING .* LETTER/} ⊆ [\p{Alphabetic}\p{Diacritic}]
 
+## Consistency of Lowercase with decompositions.
+# Note that the same is not true of Uppercase.
+# A non-lowercase character has non-lowercase characters in its decomposition,
+# or its decomposition is <square> (㋍ etc.).
+In [\P{Lowercase} - \p{dt=square}], \p{Lowercase} * toNFKD ≠ toNFKD
+
 ## Joining_Type and Joining_Group
 # Where defined, the Joining_Group refines the Joining_Type.
 OnPairsOf \P{Joining_Group=No_Joining_Group}, EqualityOf Joining_Group ⇒ EqualityOf Joining_Type