diff --git a/README-CMake.md b/README-CMake.md
index 7550808fc..715cacad2 100644
--- a/README-CMake.md
+++ b/README-CMake.md
@@ -266,6 +266,8 @@ The following useful options can be passed to CMake whilst configuring.
     Disabling this is useful for faster incremental builds. The documentation can be manually built by invoking the ``api_docs`` target.
 * ``LINK_TIME_OPTIMIZATION`` - BOOL. If set to ``TRUE`` link time optimization will be enabled.
 * ``API_LOG_SYNC`` - BOOL. If set to ``TRUE`` will enable experimental API log sync feature.
+* ``WARNINGS_AS_ERRORS`` - STRING. If set to ``TRUE`` compiler warnings will be treated as errors. If set to ``False`` compiler warnings will not be treated as errors.
+    If set to ``SERIOUS_ONLY`` a subset of compiler warnings will be treated as errors.
 
 On the command line these can be passed to ``cmake`` using the ``-D`` option. In ``ccmake`` and ``cmake-gui`` these can be set in the user interface.
 
@@ -381,3 +383,13 @@ It is tempting use file-globbing in ``CMakeLists.txt`` to find a set for files m
 use them as the sources to build a target. This however is a bad idea because it prevents CMake from knowing when it needs to rerun itself. This is why source file names are explicitly listed in the ``CMakeLists.txt`` so that when changes are made the source files used to build a target automatically triggers a rerun of CMake.
 
 Long story short. Don't use file globbing.
+
+### Serious warning flags
+
+By default the `WARNINGS_AS_ERRORS` flag is set to `SERIOUS_ONLY` which means
+some warnings will be treated as errors. These warnings are controlled by the
+relevant `*_WARNINGS_AS_ERRORS` list defined in
+`cmake/compiler_warnings.cmake`.
+
+Additional warnings should only be added here if the warnings has no false
+positives.
diff --git a/cmake/compiler_warnings.cmake b/cmake/compiler_warnings.cmake
index e02b28b2c..183f490dd 100644
--- a/cmake/compiler_warnings.cmake
+++ b/cmake/compiler_warnings.cmake
@@ -1,17 +1,61 @@
+################################################################################
+# Compiler warning flags
+################################################################################
+# These are passed to relevant compiler provided they are supported
 set(GCC_AND_CLANG_WARNINGS
-    "-Wall"
+  "-Wall"
 )
 set(GCC_ONLY_WARNINGS "")
 set(CLANG_ONLY_WARNINGS "")
 set(MSVC_WARNINGS "/W3")
 
+################################################################################
+# Serious warnings
+################################################################################
+# This declares the flags that are passed to the compiler when
+# `WARNINGS_AS_ERRORS` is set to `SERIOUS_ONLY`. Only flags that are supported
+# by the compiler are used.
+#
+# In effect this a "whitelist" approach where we explicitly tell the compiler
+# which warnings we want to be treated as errors. The alternative would be a
+# "blacklist" approach where we ask the compiler to treat all warnings are
+# treated as errors but then we explicitly list which warnings which should be
+# allowed.
+#
+# The "whitelist" approach seems simpiler because we can incrementally add
+# warnings we "think are serious".
+
+# TODO: Add more warnings that are considered serious enough that we should
+# treat them as errors.
+set(GCC_AND_CLANG_WARNINGS_AS_ERRORS
+  # https://clang.llvm.org/docs/DiagnosticsReference.html#wodr
+  "-Werror=odr"
+)
+set(GCC_WARNINGS_AS_ERRORS
+  ""
+)
+set(CLANG_WARNINGS_AS_ERRORS
+  # https://clang.llvm.org/docs/DiagnosticsReference.html#wdelete-non-virtual-dtor
+  "-Werror=delete-non-virtual-dtor"
+  # https://clang.llvm.org/docs/DiagnosticsReference.html#woverloaded-virtual
+  "-Werror=overloaded-virtual"
+)
+
+################################################################################
+# Test warning/error flags
+################################################################################
 set(WARNING_FLAGS_TO_CHECK "")
+set(WARNING_AS_ERROR_FLAGS_TO_CHECK "")
 if ("${CMAKE_CXX_COMPILER_ID}" MATCHES "GNU")
   list(APPEND WARNING_FLAGS_TO_CHECK ${GCC_AND_CLANG_WARNINGS})
   list(APPEND WARNING_FLAGS_TO_CHECK ${GCC_ONLY_WARNINGS})
+  list(APPEND WARNING_AS_ERROR_FLAGS_TO_CHECK ${GCC_AND_CLANG_WARNINGS_AS_ERRORS})
+  list(APPEND WARNING_AS_ERROR_FLAGS_TO_CHECK ${GCC_WARNINGS_AS_ERRORS})
 elseif ("${CMAKE_CXX_COMPILER_ID}" MATCHES "Clang")
   list(APPEND WARNING_FLAGS_TO_CHECK ${GCC_AND_CLANG_WARNINGS})
   list(APPEND WARNING_FLAGS_TO_CHECK ${CLANG_ONLY_WARNINGS})
+  list(APPEND WARNING_AS_ERROR_FLAGS_TO_CHECK ${GCC_AND_CLANG_WARNINGS_AS_ERRORS})
+  list(APPEND WARNING_AS_ERROR_FLAGS_TO_CHECK ${CLANG_WARNINGS_AS_ERRORS})
   # FIXME: Remove "x.." when CMP0054 is set to NEW
 elseif ("x${CMAKE_CXX_COMPILER_ID}" STREQUAL "xMSVC")
   list(APPEND WARNING_FLAGS_TO_CHECK ${MSVC_WARNINGS})
@@ -31,8 +75,40 @@ foreach (flag ${WARNING_FLAGS_TO_CHECK})
   z3_add_cxx_flag("${flag}")
 endforeach()
 
-option(WARNINGS_AS_ERRORS "Treat compiler warnings as errors" OFF)
-if (WARNINGS_AS_ERRORS)
+# TODO: Remove this eventually.
+# Detect legacy `WARNINGS_AS_ERRORS` boolean option and covert to new
+# to new option type.
+get_property(
+  WARNINGS_AS_ERRORS_CACHE_VAR_TYPE
+  CACHE
+  WARNINGS_AS_ERRORS
+  PROPERTY
+  TYPE
+)
+if ("${WARNINGS_AS_ERRORS_CACHE_VAR_TYPE}" STREQUAL "BOOL")
+  message(WARNING "Detected legacy WARNINGS_AS_ERRORS option. Upgrading")
+  set(WARNINGS_AS_ERRORS_DEFAULT "${WARNINGS_AS_ERRORS}")
+  # Delete old entry
+  unset(WARNINGS_AS_ERRORS CACHE)
+else()
+  set(WARNINGS_AS_ERRORS_DEFAULT "SERIOUS_ONLY")
+endif()
+
+set(WARNINGS_AS_ERRORS
+  ${WARNINGS_AS_ERRORS_DEFAULT}
+  CACHE STRING
+  "Treat warnings as errors. ON, OFF, or SERIOUS_ONLY"
+)
+ # Set GUI options
+set_property(
+  CACHE
+  WARNINGS_AS_ERRORS
+  PROPERTY STRINGS
+  "ON;OFF;SERIOUS_ONLY"
+)
+
+if ("${WARNINGS_AS_ERRORS}" STREQUAL "ON")
+  message(STATUS "Treating compiler warnings as errors")
   if (("${CMAKE_CXX_COMPILER_ID}" MATCHES "Clang") OR ("${CMAKE_CXX_COMPILER_ID}" MATCHES "GNU"))
     list(APPEND Z3_COMPONENT_CXX_FLAGS "-Werror")
     # FIXME: Remove "x.." when CMP0054 is set to NEW
@@ -41,8 +117,14 @@ if (WARNINGS_AS_ERRORS)
   else()
     message(AUTHOR_WARNING "Unknown compiler")
   endif()
-  message(STATUS "Treating compiler warnings as errors")
-else()
+elseif ("${WARNINGS_AS_ERRORS}" STREQUAL "SERIOUS_ONLY")
+  message(STATUS "Treating only serious compiler warnings as errors")
+  # Loop through the flags
+  foreach (flag ${WARNING_AS_ERROR_FLAGS_TO_CHECK})
+    # Add globally because some flags need to be passed at link time.
+    z3_add_cxx_flag("${flag}" GLOBAL)
+  endforeach()
+elseif ("${WARNINGS_AS_ERRORS}" STREQUAL "OFF")
   message(STATUS "Not treating compiler warnings as errors")
   # FIXME: Remove "x.." when CMP0054 is set to NEW
   if ("x${CMAKE_CXX_COMPILER_ID}" STREQUAL "xMSVC")
@@ -51,4 +133,8 @@ else()
     # build system.
     list(APPEND Z3_COMPONENT_CXX_FLAGS "/WX-")
   endif()
+else()
+  message(FATAL_ERROR
+    "WARNINGS_AS_ERRORS set to unsupported value \"${WARNINGS_AS_ERRORS}\""
+  )
 endif()
diff --git a/cmake/z3_add_cxx_flag.cmake b/cmake/z3_add_cxx_flag.cmake
index 6e756d3b9..d2624d890 100644
--- a/cmake/z3_add_cxx_flag.cmake
+++ b/cmake/z3_add_cxx_flag.cmake
@@ -2,7 +2,7 @@ include(CheckCXXCompilerFlag)
 include(CMakeParseArguments)
 
 function(z3_add_cxx_flag flag)
-  CMAKE_PARSE_ARGUMENTS(z3_add_flag "REQUIRED" "" "" ${ARGN})
+  CMAKE_PARSE_ARGUMENTS(z3_add_flag "REQUIRED;GLOBAL" "" "" ${ARGN})
   string(REPLACE "-" "_" SANITIZED_FLAG_NAME "${flag}")
   string(REPLACE "/" "_" SANITIZED_FLAG_NAME "${SANITIZED_FLAG_NAME}")
   string(REPLACE "=" "_" SANITIZED_FLAG_NAME "${SANITIZED_FLAG_NAME}")
@@ -16,8 +16,13 @@ function(z3_add_cxx_flag flag)
   endif()
   if (HAS_${SANITIZED_FLAG_NAME})
     message(STATUS "C++ compiler supports ${flag}")
-    list(APPEND Z3_COMPONENT_CXX_FLAGS "${flag}")
-    set(Z3_COMPONENT_CXX_FLAGS "${Z3_COMPONENT_CXX_FLAGS}" PARENT_SCOPE)
+    if (z3_add_flag_GLOBAL)
+      # Set globally
+      set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${flag} " PARENT_SCOPE)
+    else()
+      list(APPEND Z3_COMPONENT_CXX_FLAGS "${flag}")
+      set(Z3_COMPONENT_CXX_FLAGS "${Z3_COMPONENT_CXX_FLAGS}" PARENT_SCOPE)
+    endif()
   else()
     message(STATUS "C++ compiler does not support ${flag}")
   endif()
diff --git a/contrib/ci/Dockerfiles/z3_build.Dockerfile b/contrib/ci/Dockerfiles/z3_build.Dockerfile
index 8b922edff..2d16d5394 100644
--- a/contrib/ci/Dockerfiles/z3_build.Dockerfile
+++ b/contrib/ci/Dockerfiles/z3_build.Dockerfile
@@ -28,6 +28,7 @@ ARG Z3_INSTALL_PREFIX=/usr
 ARG Z3_STATIC_BUILD=0
 # Blank default indicates use latest.
 ARG Z3_SYSTEM_TEST_GIT_REVISION
+ARG Z3_WARNINGS_AS_ERRORS=SERIOUS_ONLY
 ARG Z3_VERBOSE_BUILD_OUTPUT=0
 
 ENV \
@@ -55,6 +56,7 @@ ENV \
   Z3_STATIC_BUILD=${Z3_STATIC_BUILD} \
   Z3_SYSTEM_TEST_DIR=/home/user/z3_system_test \
   Z3_SYSTEM_TEST_GIT_REVISION=${Z3_SYSTEM_TEST_GIT_REVISION} \
+  Z3_WARNINGS_AS_ERRORS=${Z3_WARNINGS_AS_ERRORS} \
   Z3_INSTALL_PREFIX=${Z3_INSTALL_PREFIX}
 
 # We add context across incrementally to maximal cache reuse
diff --git a/contrib/ci/README.md b/contrib/ci/README.md
index 31bb504b6..2e117c8b1 100644
--- a/contrib/ci/README.md
+++ b/contrib/ci/README.md
@@ -43,6 +43,7 @@ the future.
 * `Z3_VERBOSE_BUILD_OUTPUT` - Show compile commands in CMake builds (`0` or `1`)
 * `Z3_STATIC_BUILD` - Build Z3 binaries and libraries statically (`0` or `1`)
 * `Z3_SYSTEM_TEST_GIT_REVISION` - Git revision of [z3test](https://github.com/Z3Prover/z3test). If empty lastest revision will be used.
+* `Z3_WARNINGS_AS_ERRORS` - Set the `WARNINGS_AS_ERRORS` CMake option pased to Z3 (`OFF`, `ON`, or `SERIOUS_ONLY`)
 
 ### Linux
 
diff --git a/contrib/ci/scripts/build_z3_cmake.sh b/contrib/ci/scripts/build_z3_cmake.sh
index 98a9724c7..76fd0fb84 100755
--- a/contrib/ci/scripts/build_z3_cmake.sh
+++ b/contrib/ci/scripts/build_z3_cmake.sh
@@ -20,7 +20,8 @@ set -o pipefail
 : ${DOTNET_BINDINGS?"DOTNET_BINDINGS must be specified"}
 : ${JAVA_BINDINGS?"JAVA_BINDINGS must be specified"}
 : ${USE_LTO?"USE_LTO must be specified"}
-: ${Z3_INSTALL_PREFIX?"Z3_INSTALL_PREFIX"}
+: ${Z3_INSTALL_PREFIX?"Z3_INSTALL_PREFIX must be specified"}
+: ${Z3_WARNINGS_AS_ERRORS?"Z3_WARNINGS_AS_ERRORS must be specified"}
 
 ADDITIONAL_Z3_OPTS=()
 
@@ -120,6 +121,7 @@ cmake \
   -DCMAKE_BUILD_TYPE=${Z3_BUILD_TYPE} \
   -DPYTHON_EXECUTABLE=${PYTHON_EXECUTABLE} \
   -DCMAKE_INSTALL_PREFIX=${Z3_INSTALL_PREFIX} \
+  -DWARNINGS_AS_ERRORS=${Z3_WARNINGS_AS_ERRORS} \
   "${ADDITIONAL_Z3_OPTS[@]}" \
   "${Z3_SRC_DIR}"
 
diff --git a/contrib/ci/scripts/travis_ci_linux_entry_point.sh b/contrib/ci/scripts/travis_ci_linux_entry_point.sh
index 21b97788f..84b2dd400 100755
--- a/contrib/ci/scripts/travis_ci_linux_entry_point.sh
+++ b/contrib/ci/scripts/travis_ci_linux_entry_point.sh
@@ -120,6 +120,13 @@ if [ -n "${NO_SUPPRESS_OUTPUT}" ]; then
   )
 fi
 
+if [ -n "${Z3_WARNINGS_AS_ERRORS}" ]; then
+  BUILD_OPTS+=( \
+    "--build-arg" \
+    "Z3_WARNINGS_AS_ERRORS=${Z3_WARNINGS_AS_ERRORS}" \
+  )
+fi
+
 case ${LINUX_BASE} in
   ubuntu_14.04)
     BASE_DOCKER_FILE="${DOCKER_FILE_DIR}/z3_base_ubuntu_14.04.Dockerfile"