The　diagnosis　of　gear　and　bearing　compound　faults　remains　a　challenge　in　severe　working　conditions.　Adapted　dictionary-free　orthogonal　matching　pursuit　(ADOMP)　can　reconstruct　the　fault　signal　more　flexibly　without　predefined　dictionaries　and　maintain　the　majority　of　the　original　information,　but　it　lacks　the　ability　to　effectively　identify　the　fault-related　atoms.　A　novel　atom　selection　strategy　is　proposed　based　on　the　spectral　negentropy　of　the　squared　envelope　spectrum　(SN-SES),　which　is　sensitive　to　signal　periodicity.　The　proposed　method　can　isolate　atoms　according　to　the　characteristics　of　gear　and　bearing　vibration　signals.　To　better　match　the　fault-related　atoms,　the　minimum　entropy　deconvolution　adjusted　(MEDA)　method　is　utilized　to　preprocess　the　raw　signals,　in　which　the　filter　length　as　the　key　parameter　is　optimized　by　SN-SES　for　impulsiveness　enhancement　of　each　single　fault.　The　results　of　simulation　analysis　and　experimental　verification　confirm　the　superiority　of　the　proposed　compound-fault　diagnosis　method.