diff --git a/data-checked.cabal b/data-checked.cabal
--- a/data-checked.cabal
+++ b/data-checked.cabal
@@ -1,5 +1,5 @@
 Name: data-checked
-Version: 0.2
+Version: 0.3
 Category: Data
 Stability: experimental
 Synopsis: Type-indexed runtime-checked properties 
@@ -30,4 +30,5 @@
   GHC-Options: -Wall
   Exposed-Modules:
     Data.Checked
+    Data.Checked.Strict
 
diff --git a/src/Data/Checked.hs b/src/Data/Checked.hs
--- a/src/Data/Checked.hs
+++ b/src/Data/Checked.hs
@@ -60,4 +60,3 @@
 check v | holds (undefined ∷ p) v = Just (Checked v)
         | otherwise               = Nothing
 {-# INLINABLE check #-}
-
diff --git a/src/Data/Checked/Strict.hs b/src/Data/Checked/Strict.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Checked/Strict.hs
@@ -0,0 +1,56 @@
+{-# LANGUAGE UnicodeSyntax #-}
+{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+
+-- | A version of 'DC.Checked' that requires client code to provide
+--   a non-bottom value of the property index type to use @trust*@
+--   functions.
+module Data.Checked.Strict
+  ( Checked
+  , trustThat
+  , trustMap
+  , checked
+  , Property(..)
+  , maybeHolds
+  , check
+  , relax
+  ) where
+
+import Data.Typeable (Typeable)
+import Control.DeepSeq (NFData(..))
+import Data.Checked (Property(..), maybeHolds)
+import qualified Data.Checked as DC
+
+-- | Wrapper-evidence for property /p/.
+newtype Checked p v = Checked v deriving Typeable
+
+instance NFData v ⇒ NFData (Checked p v) where
+  rnf (Checked v) = rnf v
+
+-- | Use when the property can be deduced without a runtime check.
+--   Note that /p/ is evaluated to WHNF, so you can't use 'undefined'.
+trustThat ∷ p → v → Checked p v
+trustThat p v = p `seq` Checked v
+{-# INLINE trustThat #-}
+
+-- | Apply a fuction that preserves the property to the checked value.
+--   Note that /p/ is evaluated to WHNF, so you can't use 'undefined'.
+trustMap ∷ p → (v → v) → Checked p v → Checked p v
+trustMap p f (Checked v) = p `seq` Checked (f v)
+{-# INLINE trustMap #-}
+
+-- | Unwrap the checked value.
+checked ∷ Checked p v → v
+checked (Checked v) = v
+{-# INLINE checked #-}
+
+-- | Wrap the value if the property holds.
+check ∷ ∀ p v . Property p v ⇒ v → Maybe (Checked p v)
+check v | holds (undefined ∷ p) v = Just (Checked v)
+        | otherwise               = Nothing
+{-# INLINABLE check #-}
+
+-- | Rewrap a value into the less strict 'DC.Checked' type.
+relax ∷ Checked p v → DC.Checked p v
+relax (Checked v) = DC.trustMe v
+{-# INLINE relax #-}