diff --git a/.travis-setup.sh b/.travis-setup.sh
deleted file mode 100755
index e694e093..00000000
--- a/.travis-setup.sh
+++ /dev/null
@@ -1,10 +0,0 @@
-#!/bin/sh
-
-set -eux
-
-mkdir -p $HOME/.cabal
-cat > $HOME/.cabal/config <<EOF
-remote-repo: hackage.haskell.org:http://hackage.fpcomplete.com/
-remote-repo-cache: $HOME/.cabal/packages
-jobs: \$ncpus
-EOF
diff --git a/.travis.yml b/.travis.yml
index 23068c17..09b196d4 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,33 +1,36 @@
-# NB: don't set `language: haskell` here
+# Use new container infrastructure to enable caching
+sudo: false
 
-# The following enables several GHC versions to be tested; often it's enough to test only against the last release in a major GHC version. Feel free to omit lines listings versions you don't need/want testing for.
+# Choose a lightweight base image; we provide our own build tools.
+language: c
+
+# GHC depends on GMP. You can add other dependencies here as well.
+addons:
+  apt:
+    packages:
+    - libgmp-dev
+
+# The different configurations we want to test. You could also do things like
+# change flags or use --stack-yaml to point to a different file.
 env:
- #- CABALVER=1.20 GHCVER=7.6.3
- - CABALVER=1.20 GHCVER=7.8.4
- - CABALVER=1.22 GHCVER=7.10.1
- - CABALVER=1.22 GHCVER=7.10.2
- #- CABALVER=head GHCVER=head   # see section about GHC HEAD snapshots
+- ARGS=""
+- ARGS="--resolver lts-2"
+- ARGS="--resolver lts-3"
+- ARGS="--resolver lts"
+- ARGS="--resolver nightly"
 
-# Note: the distinction between `before_install` and `install` is not important.
 before_install:
- - travis_retry sudo add-apt-repository -y ppa:hvr/ghc
- - travis_retry sudo apt-get update
- - travis_retry sudo apt-get install cabal-install-$CABALVER ghc-$GHCVER # see note about happy/alex
- - export PATH=/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$HOME/.cabal/bin:$PATH
- - export PATH=$HOME/.cabal/bin:/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$PATH
- - ./.travis-setup.sh
+# Download and unpack the stack executable
+- mkdir -p ~/.local/bin
+- export PATH=$HOME/.local/bin:$PATH
+- travis_retry curl -L https://www.stackage.org/stack/linux-x86_64 | tar xz --wildcards --strip-components=1 -C ~/.local/bin '*/stack'
 
+# This line does all of the work: installs GHC if necessary, build the library,
+# executables, and test suites, and runs the test suites. --no-terminal works
+# around some quirks in Travis's terminal implementation.
+script: stack $ARGS --no-terminal --install-ghc test --haddock
 
-install:
- - cabal --version
- - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]"
- - travis_retry cabal update
- - travis_retry curl -L http://download.fpcomplete.com/michael/cabal-meta.tar.gz > cabal-meta.tar.gz
- - mkdir -p $HOME/.cabal/bin
- - tar zxfv cabal-meta.tar.gz -C $HOME/.cabal/bin
- - cabal install alex happy
-
-# Here starts the actual work to be performed for the package under test; any command which exits with a non-zero exit code causes the build to fail.
-script:
- - cabal-meta install --only-dependencies --enable-tests --enable-benchmarks --force-reinstalls
- - cabal-meta install --run-tests
+# Caching so the next build will be fast too.
+cache:
+  directories:
+  - $HOME/.stack