diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,2 +1,5 @@
+# monad-time-effectful-1.0.1.0 (2026-03-25)
+* Add the `runFixedStepTime` handler.
+
 # monad-time-effectful-1.0.0.0 (2023-06-19)
 * Initial release.
diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -1,8 +1,7 @@
 # monad-time-effectful
 
-[![Build Status](https://github.com/haskell-effectful/monad-time-effectful/workflows/Haskell-CI/badge.svg?branch=master)](https://github.com/haskell-effectful/monad-time-effectful/actions?query=branch%3Amaster)
+[![CI](https://github.com/haskell-effectful/monad-time-effectful/actions/workflows/haskell-ci.yml/badge.svg?branch=master)](https://github.com/haskell-effectful/monad-time-effectful/actions/workflows/haskell-ci.yml)
 [![Hackage](https://img.shields.io/hackage/v/monad-time-effectful.svg)](https://hackage.haskell.org/package/monad-time-effectful)
-[![Dependencies](https://img.shields.io/hackage-deps/v/monad-time-effectful.svg)](https://packdeps.haskellers.com/feed?needle=andrzej@rybczak.net)
 [![Stackage LTS](https://www.stackage.org/package/monad-time-effectful/badge/lts)](https://www.stackage.org/lts/package/monad-time-effectful)
 [![Stackage Nightly](https://www.stackage.org/package/monad-time-effectful/badge/nightly)](https://www.stackage.org/nightly/package/monad-time-effectful)
 
diff --git a/monad-time-effectful.cabal b/monad-time-effectful.cabal
--- a/monad-time-effectful.cabal
+++ b/monad-time-effectful.cabal
@@ -1,7 +1,7 @@
-cabal-version:      2.4
+cabal-version:      3.0
 build-type:         Simple
 name:               monad-time-effectful
-version:            1.0.0.0
+version:            1.0.1.0
 license:            MIT
 license-file:       LICENSE
 category:           Control
@@ -16,7 +16,7 @@
   CHANGELOG.md
   README.md
 
-tested-with: GHC ==8.8.4 || ==8.10.7 || ==9.0.2 || ==9.2.8 || ==9.4.5 || ==9.6.2
+tested-with: GHC == { 8.10.7, 9.0.2, 9.2.8, 9.4.8, 9.6.7, 9.8.4, 9.10.3, 9.12.2, 9.14.1 }
 
 bug-reports: https://github.com/haskell-effectful/monad-time-effectful/issues
 source-repository head
diff --git a/src/Effectful/Time.hs b/src/Effectful/Time.hs
--- a/src/Effectful/Time.hs
+++ b/src/Effectful/Time.hs
@@ -10,6 +10,7 @@
     -- ** Handlers
   , runTime
   , runFrozenTime
+  , runFixedStepTime
   ) where
 
 import Control.Monad.IO.Class
@@ -17,6 +18,7 @@
 import Data.Time
 import Effectful
 import Effectful.Dispatch.Dynamic
+import Effectful.State.Static.Local
 import GHC.Clock (getMonotonicTime)
 
 -- | Provide the ability to use the 'MonadTime' instance of 'Eff'.
@@ -39,6 +41,18 @@
 runFrozenTime time = interpret $ \_ -> \case
   CurrentTime -> pure time
   MonotonicTime -> liftIO getMonotonicTime
+
+-- | Run the 'Time' effect with a given starting time; time advances
+-- by a fixed increment for every invocation of the 'CurrentTime'
+-- operation. A negative increment will make the clock run backwards.
+--
+-- /Note:/ the 'MonotonicTime' operation works the same way as in
+-- 'runTime'.
+runFixedStepTime :: IOE :> es => UTCTime -> NominalDiffTime -> Eff (Time : es) a -> Eff es a
+runFixedStepTime start diff =
+  reinterpret_ (evalState start) $ \case
+    CurrentTime -> state $ \s -> (s, diff `addUTCTime` s)
+    MonotonicTime -> liftIO getMonotonicTime
 
 ----------------------------------------
 -- Orphan instance