diff --git a/tests/Properties.hs b/tests/Properties.hs
new file mode 100644
--- /dev/null
+++ b/tests/Properties.hs
@@ -0,0 +1,78 @@
+-- Tester beware!
+--
+-- Many of the tests below are "weak", i.e. they ensure that functions
+-- return results, without checking whether the results are correct.
+-- Weak tests are described as such.
+
+{-# LANGUAGE OverloadedStrings #-}
+{-# OPTIONS_GHC -fno-warn-missing-signatures #-}
+module Properties (tests) where
+
+import Control.DeepSeq (NFData(..))
+import Data.Function (on)
+import Data.Maybe (fromMaybe)
+import Data.Text (Text)
+import Data.Text.ICU (NormalizationMode(..))
+import QuickCheckUtils ()
+import Test.Framework (Test, testGroup)
+import Test.Framework.Providers.QuickCheck2 (testProperty)
+import qualified Data.Text as T
+import qualified Data.Text.Encoding as T
+import qualified Data.Text.ICU as I
+
+t_rnf :: (NFData a) => (Text -> a) -> Text -> Bool
+t_rnf f t = rnf (f t) == ()
+
+t_nonEmpty :: (Text -> Text) -> Text -> Bool
+t_nonEmpty f t
+    | T.null t  = T.null ft
+    | otherwise = T.length ft > 0
+  where ft = f t
+
+-- Case mapping
+
+-- These tests are all fairly weak.
+
+t_toCaseFold bool = t_nonEmpty $ I.toCaseFold bool
+t_toLower locale = t_nonEmpty $ I.toLower locale
+t_toUpper locale = t_nonEmpty $ I.toUpper locale
+
+-- Iteration
+
+t_charIterator_String a b = (compare `on` I.fromString) a b == compare a b
+t_charIterator_Text a b = (compare `on` I.fromText) a b == compare a b
+t_charIterator_Utf8 a b = (compare `on` I.fromUtf8) ba bb == compare ba bb
+  where ba = T.encodeUtf8 a; bb = T.encodeUtf8 b
+
+-- Normalization
+
+t_normalize mode = t_nonEmpty $ I.normalize mode
+
+t_quickCheck_isNormalized mode normMode txt
+  | mode `elem` [NFD, NFKD, FCD]
+              =                        quickCheck == Just isNormalized
+  | otherwise = fromMaybe isNormalized quickCheck ==      isNormalized
+  where quickCheck   = I.quickCheck mode normTxt
+        isNormalized = I.isNormalized mode normTxt
+        normTxt      = I.normalize normMode txt
+
+-- Collation
+
+-- This test is weak.
+
+t_collate_root txt = t_rnf $ I.collate I.uca txt
+
+
+tests :: Test
+tests =
+  testGroup "Properties" [
+    testProperty "t_toCaseFold" t_toCaseFold
+  , testProperty "t_toLower" t_toLower
+  , testProperty "t_toUpper" t_toUpper
+  , testProperty "t_charIterator_String" t_charIterator_String
+  , testProperty "t_charIterator_Text" t_charIterator_Text
+  , testProperty "t_charIterator_Utf8" t_charIterator_Utf8
+  , testProperty "t_normalize" t_normalize
+  , testProperty "t_quickCheck_isNormalized" t_quickCheck_isNormalized
+  , testProperty "t_collate_root" t_collate_root
+  ]
diff --git a/tests/QuickCheckUtils.hs b/tests/QuickCheckUtils.hs
new file mode 100644
--- /dev/null
+++ b/tests/QuickCheckUtils.hs
@@ -0,0 +1,27 @@
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module QuickCheckUtils () where
+
+import Control.Applicative ((<$>))
+import Control.DeepSeq (NFData(..))
+import Data.Text.ICU (Collator, LocaleName(..), NormalizationMode(..))
+import Data.Text.ICU.Break (available)
+import Test.QuickCheck (Arbitrary(..), elements)
+import qualified Data.Text as T
+import qualified Data.Text.ICU as I
+
+instance NFData Ordering where
+    rnf v  = v `seq` ()
+
+instance Arbitrary T.Text where
+    arbitrary = T.pack `fmap` arbitrary
+    shrink = map T.pack . shrink . T.unpack
+
+instance Arbitrary LocaleName where
+    arbitrary = elements (Root:available)
+
+instance Arbitrary NormalizationMode where
+    arbitrary = elements [None ..FCD]
+
+instance Arbitrary Collator where
+    arbitrary = I.collator <$> arbitrary
diff --git a/text-icu.cabal b/text-icu.cabal
--- a/text-icu.cabal
+++ b/text-icu.cabal
@@ -1,5 +1,5 @@
 name:           text-icu
-version:        0.6.3.6
+version:        0.6.3.7
 synopsis:       Bindings to the ICU library
 homepage:       https://github.com/bos/text-icu
 bug-reports:    https://github.com/bos/text-icu/issues
@@ -86,6 +86,7 @@
   type:             exitcode-stdio-1.0
   hs-source-dirs:   tests
   main-is:          Tests.hs
+  other-modules:    Properties QuickCheckUtils
 
   ghc-options:
     -Wall -threaded -O0 -rtsopts