diff --git a/.travis.yml b/.travis.yml
index f853c3cd..e0442ed8 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -88,6 +88,8 @@ install:
   - travis_retry sudo luarocks install busted
   # Install luacheck for "make check-qa".
   - if [ "$DO_CHECKQA" = 1 ]; then travis_retry sudo luarocks install luacheck; fi
+  # Install depgraph for "make check-qa".
+  - if [ "$DO_CHECKQA" = 1 ]; then travis_retry sudo luarocks install depgraph; fi
 
   # Install ldoc for building docs.
   - |
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 5fd05c9d..f963539a 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -381,6 +381,13 @@ add_custom_target(check-integration
     COMMENT "Running integration tests"
     USES_TERMINAL
     VERBATIM)
+add_custom_target(check-requires
+    lua "${CMAKE_SOURCE_DIR}/build-utils/check_for_invalid_requires.lua"
+    WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}
+    COMMENT "Checking use of require()"
+    USES_TERMINAL
+    VERBATIM)
+list(APPEND CHECK_QA_TARGETS check-requires)
 a_find_program(BUSTED_EXECUTABLE busted FALSE)
 if(BUSTED_EXECUTABLE)
     # Keep the arguments in sync with the version below!
diff --git a/build-utils/check_for_invalid_requires.lua b/build-utils/check_for_invalid_requires.lua
new file mode 100755
index 00000000..a5ec5b19
--- /dev/null
+++ b/build-utils/check_for_invalid_requires.lua
@@ -0,0 +1,119 @@
+#!/usr/bin/env lua
+
+-- This uses the "depgraph" package to parse all source code and look for calls
+-- to require(). For all these uses, we make sure that it is allowed by the
+-- white-list below. This is done to mitigate the risk of cyclic dependencies
+-- between modules and to (hopefully) enforce a bit of sane code structure.
+
+local have_depgraph, depgraph = pcall(require, "depgraph")
+
+if not have_depgraph then
+    print("depgraph not found")
+    print(depgraph)
+    print("(this error is non-fatal; we just skip its use)")
+    os.exit(0)
+end
+
+local allowed_deps = {
+    gears = {
+        lgi = true,
+    },
+    beautiful = {
+        gears = true,
+        lgi = true,
+    },
+    wibox = {
+        beautiful = true,
+        gears = true,
+        lgi = true,
+    },
+    awful = {
+        beautiful = true,
+        gears = true,
+        lgi = true,
+        wibox = true,
+    },
+    naughty = {
+        awful = true,
+        beautiful = true,
+        gears = true,
+        lgi = true,
+        wibox = true,
+    },
+    menubar = {
+        awful = true,
+        beautiful = true,
+        gears = true,
+        lgi = true,
+        wibox = true,
+    },
+    -- TODO: Get rid of these
+    ["beautiful.xresources"] = { ["awful.util"] = true },
+    ["gears.object"]         = { ["awful.util"] = true },
+    ["wibox.container"]      = { ["awful.util"] = true },
+    ["wibox.layout"]         = { ["awful.util"] = true },
+    ["wibox.widget"]         = { ["awful.util"] = true },
+    ["gears.surface"]        = { ["wibox.hierarchy"] = true },
+}
+
+-- Turn "foo.bar.baz" into "foo.bar". Returns nil if there is nothing more to
+-- remove.
+local function get_supermodule(module)
+    return string.match(module, "(.+)%.%a+")
+end
+
+-- Check if "module" (or one of its parents) is allowed to depend on
+-- "dependency" (or one of its parents).
+local function is_allowed(module, dependency)
+    assert(module ~= nil)
+    -- If both have a common parent, the dependency is allowed
+    do
+        local last_mod, mod = module, module
+        while mod do
+            last_mod, mod = mod, get_supermodule(mod)
+        end
+        local last_dep, dep = dependency, dependency
+        while dep do
+            last_dep, dep = dep, get_supermodule(dep)
+        end
+        if last_mod == last_dep then
+            return true
+        end
+    end
+    -- Check the allowed_deps table
+    while module ~= nil do
+        local allowed = allowed_deps[module]
+        if allowed then
+            local dep = dependency
+            while dep ~= nil do
+                if allowed[dep] then
+                    return true
+                end
+                dep = get_supermodule(dep)
+            end
+        end
+        module = get_supermodule(module)
+    end
+    return false
+end
+
+-- Generate the dependency graph
+local graph = assert(depgraph.make_graph({"lib"}, {}, "lib", nil, nil))
+
+-- Check if all require's are allowed by the above table
+local had_violation = false
+for _, module in ipairs(graph.modules) do
+    for _, dep in ipairs(module.deps) do
+        if not is_allowed(module.name, dep.name) then
+            had_violation = true
+            print(string.format("Dependency from %s onto %s is not allowed",
+                    module.name, dep.name))
+        end
+    end
+end
+
+if had_violation then
+    os.exit(1)
+end
+
+-- vim: filetype=lua:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:textwidth=80