diff --git a/.dockerignore b/.dockerignore
index eccb374e7..0de7a1d82 100644
--- a/.dockerignore
+++ b/.dockerignore
@@ -2,4 +2,4 @@
 .gitignore
 .git
 Dockerfile
-Dockerfile.centos7
+Dockerfile.centos
diff --git a/.travis.yml b/.travis.yml
index f27b0b26c..db0bcc23f 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -6,32 +6,40 @@ sudo: false
 
 matrix:
   include:
-    # test on docker+centos7
+    # test on docker+centos
     - os: linux
       compiler: clang
       services:
        - docker
       sudo: true
-      dist: trusty
-      env: DOCKERFILE=Dockerfile.centos7
+      dist: bionic
+      env: DOCKERFILE=Dockerfile.centos
       before_install: []
+      # build the builder image separately to run the tests
       install:
+        - docker build -t tippecanoe-image-builder -f ${DOCKERFILE} . --target=builder
         - docker build -t tippecanoe-image -f ${DOCKERFILE} .
+      # run tippecanoe --help to make sure runtime libs are correct
       script:
-        - docker run -it tippecanoe-image
+        - docker run -it tippecanoe-image-builder
+        - docker run -it tippecanoe-image tippecanoe --help
     # test on docker+ubuntu
     - os: linux
       compiler: clang
       services:
        - docker
       sudo: true
-      dist: trusty
+      dist: bionic
       env: DOCKERFILE=Dockerfile
       before_install: []
+      # build the builder image separately to run the tests
       install:
+        - docker build -t tippecanoe-image-builder -f ${DOCKERFILE} . --target=builder
         - docker build -t tippecanoe-image -f ${DOCKERFILE} .
+      # run tippecanoe --help to make sure runtime libs are correct
       script:
-        - docker run -it tippecanoe-image
+        - docker run -it tippecanoe-image-builder
+        - docker run -it tippecanoe-image tippecanoe --help
     # debug+integer-santizer build
     - os: linux
       compiler: clang
diff --git a/Dockerfile b/Dockerfile
index 1df89e5f1..0e17d0238 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -1,13 +1,14 @@
+# Allow setting version as an argument
+ARG UBUNTU_VERSION=20.04
+
 # Start from ubuntu
-FROM ubuntu:16.04
+FROM ubuntu:${UBUNTU_VERSION} as builder
 
 # Update repos and install dependencies
 RUN apt-get update \
-  && apt-get -y upgrade \
-  && apt-get -y install build-essential libsqlite3-dev zlib1g-dev
+  && apt-get -y install make gcc g++ libsqlite3-dev zlib1g-dev
 
-# Create a directory and copy in all files
-RUN mkdir -p /tmp/tippecanoe-src
+# Copy in all files
 WORKDIR /tmp/tippecanoe-src
 COPY . /tmp/tippecanoe-src
 
@@ -17,3 +18,15 @@ RUN make \
 
 # Run the tests
 CMD make test
+
+# Build final image
+FROM ubuntu:${UBUNTU_VERSION}
+
+# Install runtime dependencies
+RUN apt-get update \
+  && apt-get install -y libsqlite3-0 zlib1g \
+  && apt-get clean \
+  && rm -rf /var/lib/apt/lists/*
+
+# Copy built files into final image
+COPY --from=builder /usr/local/ /usr/local/
diff --git a/Dockerfile.centos b/Dockerfile.centos
new file mode 100644
index 000000000..5e48fd7b7
--- /dev/null
+++ b/Dockerfile.centos
@@ -0,0 +1,27 @@
+ARG CENTOS_VERSION=8
+
+# Start from centos
+FROM centos:${CENTOS_VERSION} as builder
+
+# Intall dependencies
+RUN yum install -y make sqlite-devel zlib-devel gcc-c++
+
+# Copy in all files
+WORKDIR /tmp/tippecanoe-src
+COPY . /tmp/tippecanoe-src
+
+# Build tippecanoe
+RUN make \
+  && make install
+
+# Run the tests
+CMD make test
+
+# Build final image
+FROM centos:${CENTOS_VERSION}
+
+# Install runtime dependencies
+RUN yum install -y sqlite-libs zlib
+
+# Copy built files into final image
+COPY --from=builder /usr/local/ /usr/local/
diff --git a/Dockerfile.centos7 b/Dockerfile.centos7
deleted file mode 100644
index c330de2f1..000000000
--- a/Dockerfile.centos7
+++ /dev/null
@@ -1,15 +0,0 @@
-FROM centos:7
-
-RUN yum install -y make sqlite-devel zlib-devel bash git gcc-c++
-
-# Create a directory and copy in all files
-RUN mkdir -p /tmp/tippecanoe-src
-WORKDIR /tmp/tippecanoe-src
-COPY . /tmp/tippecanoe-src
-
-# Build tippecanoe
-RUN make \
-  && make install
-
-# Run the tests
-CMD make test
diff --git a/README.md b/README.md
index b841509c2..1b9515a48 100644
--- a/README.md
+++ b/README.md
@@ -673,7 +673,7 @@ uses md2man (`gem install md2man`).
 
 Linux:
 
-    sudo apt-get install build-essential libsqlite3-dev zlib1g-dev
+    sudo apt-get install gcc g++ make libsqlite3-dev zlib1g-dev
 
 Then build: