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Our Compressor extension is exactly what you are looking for.
Compressor extension for Magento® is all-in-one powerful solution to merge, GZIP and minify CSS, JS files and Images. This extension will reduce number of requests sent to web server and reduce file sizes of those files.
We provide free installation and FREE LIFETIME support so that you don't have to worry about any compatibility issues with 3rd-party modules.
Moreover, we offer Turkey Magento Performace Optimization Service, which includes installation and configuration of "Full Page Cache" and ?JSS/CSS/Images Compressor" extensions, its configuration. This service also includes configuration of webserver and fixes of minor compatibility issues with 3rd-part modules and themes.