diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,5 +1,12 @@
 # Changelog for math-programming-glpk
 
+## [0.4.1] -- 5 July 2020
+
+### Fixed
+
+- Infeasible problems now produce an `Infeasible` status rather than
+  an `Error` status.
+
 ## [0.4.0] -- 5 July 2020
 
 ### Changed
diff --git a/math-programming-glpk.cabal b/math-programming-glpk.cabal
--- a/math-programming-glpk.cabal
+++ b/math-programming-glpk.cabal
@@ -1,6 +1,6 @@
 cabal-version:      1.12
 name:               math-programming-glpk
-version:            0.4.0
+version:            0.4.1
 license:            BSD3
 license-file:       LICENSE
 copyright:          2018 Patrick Steele
diff --git a/src/Math/Programming/Glpk/Internal.hs b/src/Math/Programming/Glpk/Internal.hs
--- a/src/Math/Programming/Glpk/Internal.hs
+++ b/src/Math/Programming/Glpk/Internal.hs
@@ -363,15 +363,7 @@
     Nothing            -> glp_get_obj_val problem -- There's been no solve, so who cares
 
 optimizeLP' :: Glpk SolutionStatus
-optimizeLP' =
-  let
-    convertResult :: Ptr Problem -> GlpkSimplexStatus -> IO SolutionStatus
-    convertResult problem result
-      | result == glpkSimplexSuccess =
-          glp_get_status problem >>= return . solutionStatus
-      | otherwise =
-          return Error
-  in do
+optimizeLP' = do
     -- Note that we've run an LP solve
     solveTypeRef <- asks _glpkLastSolveType
     liftIO $ writeIORef solveTypeRef (Just LP)
@@ -383,19 +375,11 @@
       control <- readIORef controlRef
       alloca $ \controlPtr -> do
         poke controlPtr control
-        result <- glp_simplex problem controlPtr
-        convertResult problem result
+        _<- glp_simplex problem controlPtr
+        glp_get_status problem >>= pure . solutionStatus
 
 optimizeIP' :: Glpk SolutionStatus
-optimizeIP' =
-  let
-    convertResult :: Ptr Problem -> GlpkMIPStatus -> IO SolutionStatus
-    convertResult problem result
-      | result == glpkMIPSuccess =
-        glp_mip_status problem >>= return . solutionStatus
-      | otherwise =
-        return Error
-  in do
+optimizeIP' = do
     -- Note that we've run a MIP solve
     solveTypeRef <- asks _glpkLastSolveType
     liftIO $ writeIORef solveTypeRef (Just MIP)
@@ -406,8 +390,8 @@
       control <- readIORef controlRef
       alloca $ \controlPtr -> do
         poke controlPtr control
-        result <- glp_intopt problem controlPtr
-        convertResult problem result
+        _ <- glp_intopt problem controlPtr
+        glp_mip_status problem >>= pure . solutionStatus
 
 setVariableBounds' :: Variable Glpk -> Bounds Double -> Glpk ()
 setVariableBounds' variable bounds =
@@ -524,6 +508,7 @@
   | status == glpkInfeasible = Infeasible
   | status == glpkNoFeasible = Infeasible
   | status == glpkUnbounded  = Unbounded
+  | status == glpkUndefined  = Infeasible
   | otherwise                = Error
 
 -- | Write out the current formulation to a file.
diff --git a/test/RegressionTests.hs b/test/RegressionTests.hs
--- a/test/RegressionTests.hs
+++ b/test/RegressionTests.hs
@@ -1,7 +1,6 @@
 module RegressionTests where
 
 import           Control.Monad.IO.Class
-
 import           Test.Tasty
 import           Test.Tasty.HUnit
 
@@ -12,6 +11,8 @@
 test_tree = testGroup "Regression tests"
             [ testCase "Free variables (LP)" testFreeVariablesLP
             , testCase "Free variables (IP)" testFreeVariablesIP
+            , testCase "Infeasible (LP)" testInfeasibleLP
+            , testCase "Infeasible (IP)" testInfeasibleIP
             ]
 
 assertFeasible :: SolutionStatus -> Glpk ()
@@ -22,14 +23,14 @@
       Infeasible -> assertFailure "Infeasible program"
       _          -> pure ()
 
-assertRunGlpk :: Glpk a -> IO ()
+assertRunGlpk :: Glpk a -> Assertion
 assertRunGlpk program = do
   eResult <- runGlpk program
   case eResult of
     Left err -> assertFailure ("Error solving program: " <> show err)
     Right _  -> pure ()
 
-testFreeVariablesLP :: IO ()
+testFreeVariablesLP :: Assertion
 testFreeVariablesLP = assertRunGlpk $ do
   x <- free
   y <- free
@@ -49,7 +50,7 @@
   liftIO $ 3.1 @=? vy
   liftIO $ -3.1 @=? vz
 
-testFreeVariablesIP :: IO ()
+testFreeVariablesIP :: Assertion
 testFreeVariablesIP = assertRunGlpk $ do
   x <- integer
   y <- integer
@@ -68,3 +69,23 @@
   liftIO $ 0 @=? vx
   liftIO $ 3 @=? vy
   liftIO $ -3 @=? vz
+
+testInfeasibleLP :: Assertion
+testInfeasibleLP = assertRunGlpk $ do
+  x <- free
+  _ <- x @>=# 2
+  _ <- x @<=# 1
+
+  status <- optimizeLP
+
+  liftIO $ Infeasible @=? status
+
+testInfeasibleIP :: Assertion
+testInfeasibleIP = assertRunGlpk $ do
+  x <- integer
+  _ <- x @>=# 2
+  _ <- x @<=# 1
+
+  status <- optimizeIP
+
+  liftIO $ Infeasible @=? status