diff --git a/Dockerfile b/Dockerfile
index b80eb78..3024b4c 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -6,7 +6,21 @@ ARG TOOLCHAIN=stable
 
 # The OpenSSL version to use. We parameterize this because many Rust
 # projects will fail to build with 1.1.
-ARG OPENSSL_VERSION=1.1.1f
+#
+# ALSO UPDATE hooks/build!
+ARG OPENSSL_VERSION=1.1.1g
+
+# Versions for other dependencies. Here are the places to check for new
+# releases:
+#
+# - https://github.com/rust-lang/mdBook/releases
+# - https://github.com/EmbarkStudios/cargo-deny/releases
+# - http://zlib.net/
+# - https://ftp.postgresql.org/pub/source/
+ARG MDBOOK_VERSION=0.3.7
+ARG CARGO_DENY_VERSION=0.6.6
+ARG ZLIB_VERSION=1.2.11
+ARG POSTGRESQL_VERSION=11.7
 
 # Make sure we have basic dev tools for building C libraries.  Our goal
 # here is to support the musl-libc builds and Cargo builds needed for a
@@ -38,16 +52,14 @@ RUN apt-get update && \
         && \
     apt-get clean && rm -rf /var/lib/apt/lists/* && \
     useradd rust --user-group --create-home --shell /bin/bash --groups sudo && \
-    MDBOOK_VERSION=0.3.6 && \
     curl -fLO https://github.com/rust-lang-nursery/mdBook/releases/download/v$MDBOOK_VERSION/mdbook-v$MDBOOK_VERSION-x86_64-unknown-linux-gnu.tar.gz && \
     tar xf mdbook-v$MDBOOK_VERSION-x86_64-unknown-linux-gnu.tar.gz && \
     mv mdbook /usr/local/bin/ && \
     rm -f mdbook-v$MDBOOK_VERSION-x86_64-unknown-linux-gnu.tar.gz && \
-    DENY_VERSION=0.6.6 && \
-    curl -fLO https://github.com/EmbarkStudios/cargo-deny/releases/download/$DENY_VERSION/cargo-deny-$DENY_VERSION-x86_64-unknown-linux-musl.tar.gz && \
-    tar xf cargo-deny-$DENY_VERSION-x86_64-unknown-linux-musl.tar.gz && \
-    mv cargo-deny-$DENY_VERSION-x86_64-unknown-linux-musl/cargo-deny /usr/local/bin/ && \
-    rm -rf cargo-deny-$DENY_VERSION-x86_64-unknown-linux-musl cargo-deny-$DENY_VERSION-x86_64-unknown-linux-musl.tar.gz 
+    curl -fLO https://github.com/EmbarkStudios/cargo-deny/releases/download/$CARGO_DENY_VERSION/cargo-deny-$CARGO_DENY_VERSION-x86_64-unknown-linux-musl.tar.gz && \
+    tar xf cargo-deny-$CARGO_DENY_VERSION-x86_64-unknown-linux-musl.tar.gz && \
+    mv cargo-deny-$CARGO_DENY_VERSION-x86_64-unknown-linux-musl/cargo-deny /usr/local/bin/ && \
+    rm -rf cargo-deny-$CARGO_DENY_VERSION-x86_64-unknown-linux-musl cargo-deny-$CARGO_DENY_VERSION-x86_64-unknown-linux-musl.tar.gz 
 
 # Static linking for C++ code
 RUN sudo ln -s "/usr/bin/g++" "/usr/bin/musl-g++"
@@ -107,7 +119,6 @@ RUN echo "Building OpenSSL" && \
 
 RUN echo "Building zlib" && \
     cd /tmp && \
-    ZLIB_VERSION=1.2.11 && \
     curl -fLO "http://zlib.net/zlib-$ZLIB_VERSION.tar.gz" && \
     tar xzf "zlib-$ZLIB_VERSION.tar.gz" && cd "zlib-$ZLIB_VERSION" && \
     CC=musl-gcc ./configure --static --prefix=/usr/local/musl && \
@@ -116,7 +127,6 @@ RUN echo "Building zlib" && \
 
 RUN echo "Building libpq" && \
     cd /tmp && \
-    POSTGRESQL_VERSION=11.2 && \
     curl -fLO "https://ftp.postgresql.org/pub/source/v$POSTGRESQL_VERSION/postgresql-$POSTGRESQL_VERSION.tar.gz" && \
     tar xzf "postgresql-$POSTGRESQL_VERSION.tar.gz" && cd "postgresql-$POSTGRESQL_VERSION" && \
     CC=musl-gcc CPPFLAGS=-I/usr/local/musl/include LDFLAGS=-L/usr/local/musl/lib ./configure --with-openssl --without-readline --prefix=/usr/local/musl && \
diff --git a/hooks/build b/hooks/build
index 5366af5..c066546 100755
--- a/hooks/build
+++ b/hooks/build
@@ -8,9 +8,11 @@
 set -euo pipefail
 
 # Default to using OpenSSL 1.1 now, because 1.0 has stopped receiving security
-# updates. 1.1 is incompatible with the crates postgres 0.15 and openssl 0.9,
-# so we do offer the option of falling back to 1.0.
-OPENSSL_VERSION=1.1.1f
+# updates. 1.1 is incompatible with the crates postgres 0.15 and openssl 0.9, so
+# we do offer the option of falling back to 1.0.
+#
+# Find the latest version at https://www.openssl.org/source/
+OPENSSL_VERSION=1.1.1g
 
 # Pick an appropriate Docker tag
 case "$DOCKER_TAG" in
@@ -19,6 +21,7 @@ case "$DOCKER_TAG" in
     ;;
   *-openssl10)
     DOCKER_TAG_WITHOUT_OPENSSL="${DOCKER_TAG/-openssl10/}"
+    # Find the latest version at https://www.openssl.org/source/old/1.0.2/
     OPENSSL_VERSION=1.0.2u
     ;;
   *)