diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,3 +1,7 @@
+## 0.7.0.3
+
+* LTS bumps: specify a goal
+
 ## 0.7.0.2
 
 * Deal better with invariant violations around unregistered packages
diff --git a/Stackage/CompleteBuild.hs b/Stackage/CompleteBuild.hs
--- a/Stackage/CompleteBuild.hs
+++ b/Stackage/CompleteBuild.hs
@@ -1,6 +1,7 @@
-{-# LANGUAGE NoImplicitPrelude #-}
-{-# LANGUAGE OverloadedStrings #-}
-{-# LANGUAGE RecordWildCards   #-}
+{-# LANGUAGE DeriveDataTypeable #-}
+{-# LANGUAGE NoImplicitPrelude  #-}
+{-# LANGUAGE OverloadedStrings  #-}
+{-# LANGUAGE RecordWildCards    #-}
 module Stackage.CompleteBuild
     ( BuildType (..)
     , BumpType (..)
@@ -45,7 +46,7 @@
     , bfBuildHoogle      :: !Bool
     } deriving (Show)
 
-data BuildType = Nightly | LTS BumpType
+data BuildType = Nightly | LTS BumpType Text
     deriving (Show, Read, Eq, Ord)
 
 data BumpType = Major | Minor
@@ -93,6 +94,20 @@
   where
     slug' = "nightly-" ++ day
 
+parseGoal :: MonadThrow m => Text -> m (LTSVer -> Bool)
+parseGoal "" = return $ const True
+parseGoal t =
+    case decimal t of
+        Right (major, "") -> return $ \(LTSVer major' _) -> major' <= major
+        _ ->
+            case parseLTSRaw t of
+                Nothing -> throwM $ ParseGoalFailure t
+                Just x -> return (< x)
+
+data ParseGoalFailure = ParseGoalFailure Text
+    deriving (Show, Typeable)
+instance Exception ParseGoalFailure
+
 getSettings :: Manager -> BuildType -> IO Settings
 getSettings man Nightly = do
     day <- tshow . utctDay <$> getCurrentTime
@@ -100,10 +115,13 @@
     pkgs <- getLatestAllowedPlans bc
     plan' <- newBuildPlan pkgs bc
     return $ nightlySettings day plan'
-getSettings man (LTS bumpType) = do
+getSettings man (LTS bumpType goal) = do
+    matchesGoal <- parseGoal goal
     Option mlts <- fmap (fmap getMax) $ runResourceT
         $ sourceDirectory "."
-       $$ foldMapC (Option . fmap Max . parseLTSVer . filename)
+       $= concatMapC (parseLTSVer . filename)
+       $= filterC matchesGoal
+       $$ foldMapC (Option . Just . Max)
 
     (new, plan') <- case bumpType of
         Major -> do
@@ -167,10 +185,15 @@
 parseLTSVer fp = do
     w <- stripPrefix "lts-" $ fpToText fp
     x <- stripSuffix ".yaml" w
+    parseLTSRaw x
+
+parseLTSRaw :: Text -> Maybe LTSVer
+parseLTSRaw x = do
     Right (major, y) <- Just $ decimal x
     z <- stripPrefix "." y
     Right (minor, "") <- Just $ decimal z
     return $ LTSVer major minor
+
 renderLTSVer :: LTSVer -> FilePath
 renderLTSVer lts = fpFromText $ concat
     [ "lts-"
diff --git a/app/stackage.hs b/app/stackage.hs
--- a/app/stackage.hs
+++ b/app/stackage.hs
@@ -44,12 +44,12 @@
                   "Build, test and upload the Nightly snapshot"
             , cmnd
                   (uncurry completeBuild)
-                  (fmap (LTS Major, ) buildFlags)
+                  (lts Major)
                   "lts-major"
                   "Build, test and upload the LTS (major) snapshot"
             , cmnd
                   (uncurry completeBuild)
-                  (fmap (LTS Minor, ) buildFlags)
+                  (lts Minor)
                   "lts-minor"
                   "Build, test and upload the LTS (minor) snapshot"
             , cmnd
@@ -208,3 +208,11 @@
                  metavar "SERVER-URL" <>
                  showDefault <> value (T.unpack $ unStackageServer def) <>
                  help "Server to upload bundle to")
+
+    lts bumpType = (\x y -> (y, x)) -- get the order of arguments correct
+        <$> buildFlags
+        <*> (LTS bumpType <$> (T.pack <$> argument str
+                ( metavar "TARGET-VERSION"
+               <> help "Used to run old LTS minor bumps, and rerun broken builds"
+               <> value ""
+                ) ) )
diff --git a/stackage-curator.cabal b/stackage-curator.cabal
--- a/stackage-curator.cabal
+++ b/stackage-curator.cabal
@@ -1,5 +1,5 @@
 name:                stackage-curator
-version:             0.7.0.2
+version:             0.7.0.3
 synopsis:            Tools for curating Stackage bundles
 description:         Please see <http://www.stackage.org/package/stackage-curator> for a description and documentation.
 homepage:            https://github.com/fpco/stackage