diff --git a/src/node/utils/Minify.js b/src/node/utils/Minify.js
index 034a225a3..a6187331d 100644
--- a/src/node/utils/Minify.js
+++ b/src/node/utils/Minify.js
@@ -414,11 +414,36 @@ function compressJS(content)
 function compressCSS(filename, content, callback)
 {
   try {
-    var base = path.join(ROOT_DIR, path.dirname(filename));
-    new CleanCSS({relativeTo: base}).minify(content, function (errors, minified) {
+    const absPath = path.join(ROOT_DIR, filename);
+
+    /*
+     * Changes done to migrate CleanCSS 3.x -> 4.x:
+     *
+     * 1. Disabling rebase is necessary because otherwise the URLs for the web
+     *    fonts become wrong.
+     *
+     *    EXAMPLE 1:
+     *        /static/css/src/static/font/fontawesome-etherpad.woff
+     *      instead of
+     *        /static/font/fontawesome-etherpad.woff
+     *    EXAMPLE 2 (this is more surprising):
+     *        /p/src/static/font/opendyslexic.otf
+     *      instead of
+     *        /static/font/opendyslexic.otf
+     *
+     * 2. CleanCSS.minify() can either receive a string containing the CSS, or
+     *    an array of strings. In that case each array element is interpreted as
+     *    an absolute local path from which the CSS file is read.
+     *
+     *    In version 4.x, CleanCSS API was simplified, eliminating the
+     *    relativeTo parameter, and thus we cannot use our already loaded
+     *    "content" argument, but we have to wrap the absolute path to the CSS
+     *    in an array and ask the library to read it by itself.
+     */
+    new CleanCSS({rebase: false}).minify([absPath], function (errors, minified) {
       if (errors) {
         // on error, just yield the un-minified original, but write a log message
-        console.error(`CleanCSS.minify() returned an error on ${filename} (base CSS path: ${base}): ${errors}`);
+        console.error(`CleanCSS.minify() returned an error on ${filename} (${absPath}): ${errors}`);
         callback(null, content);
       } else {
         callback(null, minified.styles);
@@ -426,7 +451,7 @@ function compressCSS(filename, content, callback)
     });
   } catch (error) {
     // on error, just yield the un-minified original, but write a log message
-    console.error(`Unexpected error minifying ${filename} (base CSS path: ${base}): ${error}`);
+    console.error(`Unexpected error minifying ${filename} (${absPath}): ${error}`);
     callback(null, content);
   }
 }
diff --git a/src/package-lock.json b/src/package-lock.json
index 1d1e58840..75609fc5d 100644
--- a/src/package-lock.json
+++ b/src/package-lock.json
@@ -236,11 +236,6 @@
         "repeat-string": "^1.5.2"
       }
     },
-    "amdefine": {
-      "version": "1.0.1",
-      "resolved": "https://registry.npmjs.org/amdefine/-/amdefine-1.0.1.tgz",
-      "integrity": "sha1-SlKCrBZHKek2Gbz9OtFR+BfOkfU="
-    },
     "ansi-regex": {
       "version": "2.1.1",
       "resolved": "https://registry.npmjs.org/ansi-regex/-/ansi-regex-2.1.1.tgz",
@@ -712,22 +707,11 @@
       }
     },
     "clean-css": {
-      "version": "3.4.19",
-      "resolved": "https://registry.npmjs.org/clean-css/-/clean-css-3.4.19.tgz",
-      "integrity": "sha1-wyqKE8o7gkYJsUMGpdp22Hk8eHQ=",
+      "version": "4.2.3",
+      "resolved": "https://registry.npmjs.org/clean-css/-/clean-css-4.2.3.tgz",
+      "integrity": "sha512-VcMWDN54ZN/DS+g58HYL5/n4Zrqe8vHJpGA8KdgUXFU4fuP/aHNw8eld9SyEIyabIMJX/0RaY/fplOo5hYLSFA==",
       "requires": {
-        "commander": "2.8.x",
-        "source-map": "0.4.x"
-      },
-      "dependencies": {
-        "source-map": {
-          "version": "0.4.4",
-          "resolved": "https://registry.npmjs.org/source-map/-/source-map-0.4.4.tgz",
-          "integrity": "sha1-66T12pwNyZneaAMti092FzZSA2s=",
-          "requires": {
-            "amdefine": ">=0.0.4"
-          }
-        }
+        "source-map": "~0.6.0"
       }
     },
     "cliui": {
@@ -789,12 +773,10 @@
       }
     },
     "commander": {
-      "version": "2.8.1",
-      "resolved": "https://registry.npmjs.org/commander/-/commander-2.8.1.tgz",
-      "integrity": "sha1-Br42f+v9oMMwqh4qBy09yXYkJdQ=",
-      "requires": {
-        "graceful-readlink": ">= 1.0.0"
-      }
+      "version": "2.15.1",
+      "resolved": "https://registry.npmjs.org/commander/-/commander-2.15.1.tgz",
+      "integrity": "sha512-VlfT9F3V0v+jr4yxPc5gg9s62/fIVWsd2Bk2iD435um1NlGMYdVCq+MjcXnhYq2icNOizHr1kK+5TI6H0Hy0ag==",
+      "dev": true
     },
     "commondir": {
       "version": "1.0.1",
@@ -1614,11 +1596,6 @@
       "resolved": "https://registry.npmjs.org/graceful-fs/-/graceful-fs-4.2.2.tgz",
       "integrity": "sha512-IItsdsea19BoLC7ELy13q1iJFNmd7ofZH5+X/pJr90/nRoPEX0DJo1dHDbgtYWOhJhcCgMDTOw84RZ72q6lB+Q=="
     },
-    "graceful-readlink": {
-      "version": "1.0.1",
-      "resolved": "https://registry.npmjs.org/graceful-readlink/-/graceful-readlink-1.0.1.tgz",
-      "integrity": "sha1-TK+tdrxi8C+gObL5Tpo906ORpyU="
-    },
     "growl": {
       "version": "1.10.5",
       "resolved": "https://registry.npmjs.org/growl/-/growl-1.10.5.tgz",
@@ -2388,12 +2365,6 @@
         "supports-color": "5.4.0"
       },
       "dependencies": {
-        "commander": {
-          "version": "2.15.1",
-          "resolved": "https://registry.npmjs.org/commander/-/commander-2.15.1.tgz",
-          "integrity": "sha512-VlfT9F3V0v+jr4yxPc5gg9s62/fIVWsd2Bk2iD435um1NlGMYdVCq+MjcXnhYq2icNOizHr1kK+5TI6H0Hy0ag==",
-          "dev": true
-        },
         "debug": {
           "version": "3.1.0",
           "resolved": "https://registry.npmjs.org/debug/-/debug-3.1.0.tgz",
diff --git a/src/package.json b/src/package.json
index 926de995e..7f13cf873 100644
--- a/src/package.json
+++ b/src/package.json
@@ -34,7 +34,7 @@
     "async-stacktrace": "0.0.2",
     "channels": "0.0.4",
     "cheerio": "0.20.0",
-    "clean-css": "3.4.19",
+    "clean-css": "4.2.3",
     "cookie-parser": "1.4.4",
     "ejs": "2.6.1",
     "etherpad-require-kernel": "1.0.9",