diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,20 @@
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [PVP versioning](https://pvp.haskell.org/).
 
+## v2.6.3 _(2024-09-07)_
+
+### Added
+- Added a solver configuration `bitwuzlaKissat` for `Bitwuzla` with underlying SAT-Solver `Kissat`.
+
+### Changed
+- Removed `solveMinimizedDebug` & `solveMaximizedDebug`. Use the modified `solveMinimized` & `solveMaximized` instead.
+You can also provide a step-size now.
+- Fixed a bug where `MonadOMT#solve` would run `get-model` although the solver did not necessarily respond with `Sat`.
+- `SharingMode` for sharing common (sub-)expressions now defaults to `None`.
+The previous default `StableNames` in general is only worth using, when your program can benefit a lot from sharing.
+Otherwise it may drastically downgrade solver performance due to abundance of sharing-variables.
+If you still want to use it, run `setSharingMode StableNames` within the problems monad.
+
 ## v2.6.2 _(2024-09-04)_
 
 ### Changed
diff --git a/hasmtlib.cabal b/hasmtlib.cabal
--- a/hasmtlib.cabal
+++ b/hasmtlib.cabal
@@ -1,7 +1,7 @@
 cabal-version:         3.0
 
 name:                  hasmtlib
-version:               2.6.2
+version:               2.6.3
 synopsis:              A monad for interfacing with external SMT solvers
 description:           Hasmtlib is a library for generating SMTLib2-problems using a monad.
   It takes care of encoding your problem, marshaling the data to an external solver and parsing and interpreting the result into Haskell types.
diff --git a/src/Language/Hasmtlib/Internal/Sharing.hs b/src/Language/Hasmtlib/Internal/Sharing.hs
--- a/src/Language/Hasmtlib/Internal/Sharing.hs
+++ b/src/Language/Hasmtlib/Internal/Sharing.hs
@@ -28,7 +28,7 @@
   deriving Show
 
 instance Default SharingMode where
-  def = StableNames
+  def = None
 
 -- | States that can share expressions by comparing their 'StableName's.
 class Sharing s where
diff --git a/src/Language/Hasmtlib/Solver/Bitwuzla.hs b/src/Language/Hasmtlib/Solver/Bitwuzla.hs
--- a/src/Language/Hasmtlib/Solver/Bitwuzla.hs
+++ b/src/Language/Hasmtlib/Solver/Bitwuzla.hs
@@ -9,3 +9,13 @@
 --   Make sure it's default SAT-Solver binary - probably @cadical@ - is in path too.
 bitwuzla :: Config
 bitwuzla = defaultConfig { exe = "bitwuzla", args = [] }
+
+
+-- | A 'Config' for Bitwuzla with Kissat as underlying sat-solver.
+--
+--   Requires binary @bitwuzla@ and to be in path.
+--   Will use the @kissat@ shipped with @bitwuzla@.
+--
+--   It is recommended to build @bitwuzla@ from source for this to work as expected.
+bitwuzlaKissat :: Config
+bitwuzlaKissat = defaultConfig { exe = "bitwuzla", args = ["--sat-solver=kissat"] }
diff --git a/src/Language/Hasmtlib/Type/MonadSMT.hs b/src/Language/Hasmtlib/Type/MonadSMT.hs
--- a/src/Language/Hasmtlib/Type/MonadSMT.hs
+++ b/src/Language/Hasmtlib/Type/MonadSMT.hs
@@ -36,7 +36,6 @@
 import Language.Hasmtlib.Codec
 import Data.Proxy
 import Control.Lens
-import Control.Monad
 import Control.Monad.State
 
 -- | A 'MonadState' that holds an SMT-Problem.
@@ -235,12 +234,17 @@
 -- (res, sol) <- solve
 -- case res of
 --   Sat -> do
---     x' <- getValue x
 --     liftIO $ print $ decode sol x
 --   r -> print r
 -- @
 solve :: (MonadIncrSMT s m, MonadIO m) => m (Result, Solution)
-solve = liftM2 (,) checkSat getModel
+solve = do
+  res <- checkSat
+  case res of
+    Sat -> do
+      sol <- getModel
+      return (Sat, sol)
+    r -> return (r, mempty)
 
 -- | A 'MonadSMT' that addtionally allows optimization targets.
 --
diff --git a/src/Language/Hasmtlib/Type/Solver.hs b/src/Language/Hasmtlib/Type/Solver.hs
--- a/src/Language/Hasmtlib/Type/Solver.hs
+++ b/src/Language/Hasmtlib/Type/Solver.hs
@@ -13,14 +13,13 @@
   , interactiveWith, debugInteractiveWith
 
   -- ** Minimzation
-  , solveMinimized, solveMinimizedDebug
+  , solveMinimized
 
   -- ** Maximization
-  , solveMaximized, solveMaximizedDebug
+  , solveMaximized
   )
 where
 
-import Language.Hasmtlib.Internal.Sharing
 import Language.Hasmtlib.Type.MonadSMT
 import Language.Hasmtlib.Type.Expr
 import Language.Hasmtlib.Type.SMTSort
@@ -30,6 +29,7 @@
 import qualified SMTLIB.Backends as Backend
 import qualified SMTLIB.Backends.Process as Process
 import Data.Default
+import Data.Maybe
 import Control.Monad.State
 
 -- | Data that can have a 'Backend.Solver' which may be debugged.
@@ -38,7 +38,7 @@
   withSolver :: Backend.Solver -> Bool -> a
 
 instance WithSolver Pipe where
-  withSolver = Pipe 0 Nothing StableNames mempty mempty
+  withSolver = Pipe 0 Nothing def mempty mempty
 
 -- | @'solveWith' solver prob@ solves a SMT problem @prob@ with the given
 -- @solver@. It returns a pair consisting of:
@@ -130,56 +130,111 @@
 
 -- | Solves the current problem with respect to a minimal solution for a given numerical expression.
 --
---   Uses iterative refinement.
+--   This is done by incrementally refining the upper bound for a given target.
+--   Terminates, when setting the last intermediate result as new upper bound results in 'Unsat'.
+--   Then removes that last assertion and returns the previous (now confirmed minimal) result.
 --
---   If you want access to intermediate results, use 'solveMinimizedDebug' instead.
+--   You can also provide a step-size. You do not have to worry about stepping over the optimal result.
+--   This implementation takes care of it.
+--
+--   Access to intermediate results is also possible via an 'IO'-Action.
+--
+-- ==== __Examples__
+--
+-- @
+-- x <- var \@IntSort
+-- assert $ x >? 4
+-- solveMinimized x Nothing Nothing
+-- @
+--
+-- The solver will return @x := 5@.
+--
+-- The first 'Nothing' indicates that each intermediate result will be set as next upper bound.
+-- The second 'Nothing' shows that we do not care about intermediate, but only the final (minimal) result.
+--
+-- @
+-- x <- var \@IntSort
+-- assert $ x >? 4
+-- solveMinimized x (Just (\\r -> r-1)) (Just print)
+-- @
+--
+-- The solver will still return @x := 5@.
+--
+-- However, here we want the next bound of each refinement to be @lastResult - 1@.
+-- Also, every intermediate result is printed.
 solveMinimized :: (MonadIncrSMT Pipe m, MonadIO m, KnownSMTSort t, Orderable (Expr t))
-  => Expr t
-  -> m (Result, Solution)
-solveMinimized = solveOptimized Nothing (<?)
-
--- | Like 'solveMinimized' but with access to intermediate results.
-solveMinimizedDebug :: (MonadIncrSMT Pipe m, MonadIO m, KnownSMTSort t, Orderable (Expr t))
-  => (Solution -> IO ())
-  -> Expr t
+  => Expr t                             -- ^ Target to minimize
+  -> Maybe (Expr t -> Expr t)           -- ^ Step-size: Lambda is given last result as argument, producing the next upper bound
+  -> Maybe (Solution -> IO ())          -- ^ Accessor to intermediate results
   -> m (Result, Solution)
-solveMinimizedDebug debug = solveOptimized (Just debug) (<?)
+solveMinimized = solveOptimized (<?)
 
 -- | Solves the current problem with respect to a maximal solution for a given numerical expression.
 --
---   Uses iterative refinement.
+--   This is done by incrementally refining the lower bound for a given target.
+--   Terminates, when setting the last intermediate result as new lower bound results in 'Unsat'.
+--   Then removes that last assertion and returns the previous (now confirmed maximal) result.
 --
---   If you want access to intermediate results, use 'solveMaximizedDebug' instead.
+--   You can also provide a step-size. You do not have to worry about stepping over the optimal result.
+--   This implementation takes care of it.
+--
+--   Access to intermediate results is also possible via an 'IO'-Action.
+--
+-- ==== __Examples__
+--
+-- @
+-- x <- var \@IntSort
+-- assert $ x <? 4
+-- solveMaximized x Nothing Nothing
+-- @
+--
+-- The solver will return @x := 3@.
+--
+-- The first 'Nothing' indicates that each intermediate result will be set as next lower bound.
+-- The second 'Nothing' shows that we do not care about intermediate, but only the final (maximal) result.
+--
+-- @
+-- x <- var \@IntSort
+-- assert $ x <? 4
+-- solveMinimized x (Just (+1)) (Just print)
+-- @
+--
+-- The solver will still return @x := 3@.
+--
+-- However, here we want the next bound of each refinement to be @lastResult + 1@.
+-- Also, every intermediate result is printed.
 solveMaximized :: (MonadIncrSMT Pipe m, MonadIO m, KnownSMTSort t, Orderable (Expr t))
-  => Expr t
-  -> m (Result, Solution)
-solveMaximized = solveOptimized Nothing (>?)
-
--- | Like 'solveMaximized' but with access to intermediate results.
-solveMaximizedDebug :: (MonadIncrSMT Pipe m, MonadIO m, KnownSMTSort t, Orderable (Expr t))
-  => (Solution -> IO ())
-  -> Expr t
+  => Expr t                             -- ^ Target to maximize
+  -> Maybe (Expr t -> Expr t)           -- ^ Step-size: Lambda is given last result as argument, producing the next lower bound
+  -> Maybe (Solution -> IO ())          -- ^ Accessor to intermediate results
   -> m (Result, Solution)
-solveMaximizedDebug debug = solveOptimized (Just debug) (>?)
+solveMaximized = solveOptimized (>?)
 
 solveOptimized :: (MonadIncrSMT Pipe m, MonadIO m, KnownSMTSort t)
-  => Maybe (Solution -> IO ())
-  -> (Expr t -> Expr t -> Expr BoolSort)
+  => (Expr t -> Expr t -> Expr BoolSort)
   -> Expr t
+  -> Maybe (Expr t -> Expr t)
+  -> Maybe (Solution -> IO ())
   -> m (Result, Solution)
-solveOptimized mDebug op = go Unknown mempty
+solveOptimized op goal mStep mDebug = refine Unknown mempty goal
   where
-    go oldRes oldSol target = do
-      push
-      (res, sol) <- solve
+    refine oldRes oldSol target = do
+      res <- checkSat
       case res of
         Sat   -> do
+          sol <- getModel
           case decode sol target of
             Nothing        -> return (Sat, mempty)
             Just targetSol -> do
               case mDebug of
                 Nothing    -> pure ()
                 Just debug -> liftIO $ debug sol
-              assert $ target `op` encode targetSol
-              go res sol target
-        _ -> pop >> return (oldRes, oldSol)
+              push
+              let step = fromMaybe id mStep
+              assert $ target `op` step (encode targetSol)
+              refine res sol target
+        _ -> do
+          pop
+          case mStep of
+            Nothing -> return (oldRes, oldSol)
+            Just _  -> solveOptimized op goal Nothing mDebug -- make sure the very last step did not skip the optimal result