diff --git a/System/Random/MWC/CondensedTable.hs b/System/Random/MWC/CondensedTable.hs
--- a/System/Random/MWC/CondensedTable.hs
+++ b/System/Random/MWC/CondensedTable.hs
@@ -40,6 +40,7 @@
 import qualified Data.Vector.Unboxed         as U
 import qualified Data.Vector                 as V
 import Data.Vector.Generic (Vector)
+import Numeric.SpecFunctions (logFactorial)
 
 import Prelude hiding ((++))
 
@@ -237,9 +238,11 @@
                   ++ U.tail (U.unfoldr unfoldBackward (pMax, nMax))
       where
         -- Number with highest probability and its probability
+        --
+        -- FIXME: this is not ideal precision-wise. Check if code
+        --        from statistics gives better precision.
         nMax = floor lam :: Int
-        pMax = let c = lam * exp( -lam / fromIntegral nMax )
-               in  U.foldl' (\p i -> p * c / i) 1 (U.enumFromN 1 nMax)
+        pMax = exp $ fromIntegral nMax * log lam - lam - logFactorial nMax
         -- Build probability list
         unfoldForward (p,i)
           | p < minP  = Nothing
@@ -252,6 +255,7 @@
           | otherwise = Just ( (i,p)
                              , (p / lam * fromIntegral i, i-1)
                              )
+    -- Minimal representable probability for condensed tables
     minP = 1.1641532182693481e-10 -- 2**(-33)
 
 -- | Create a lookup table for the binomial distribution.
diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -1,3 +1,8 @@
+## Changes in 0.13.6.0
+
+  * `tablePoisson` now can handle λ>1923, see #59 for details.
+    That required intoduction of dependency on math-functions.
+
 ## Changes in 0.13.5.0
 
   * `logCategorical` added
diff --git a/mwc-random.cabal b/mwc-random.cabal
--- a/mwc-random.cabal
+++ b/mwc-random.cabal
@@ -1,5 +1,5 @@
 name:           mwc-random
-version:        0.13.5.0
+version:        0.13.6.0
 synopsis:       Fast, high quality pseudo random number generation
 description:
   This package contains code for generating high quality random
@@ -44,7 +44,8 @@
     base < 5,
     primitive,
     time,
-    vector >= 0.7
+    vector         >= 0.7,
+    math-functions >= 0.2.1.0
   if impl(ghc >= 6.10)
     build-depends:
       base >= 4