A novel method to remove aluminium from the framework of as-synthesized zeolite crystals is presented. Hydrothermal treatment in an aqueous ammonium fluoride solution leads to selective dealumination of ZSM-5–TPA zeolite crystals. The optimized dealumination procedure results in 30–50% removal of Al atoms without significant structural degradation. It is also shown that template stabilization by tetrapropylammonium cations or pentaerythritol plays a key role in the developed method, as template-free ZSM-5 crystals, treated under similar conditions, lose their crystallinity and microporosity. The mild dealumination was applied to as-synthesized hierarchical mordenite zeolite to obtain a much more effective catalyst in hydroconversion of heavy paraffins. The optimized Pd/MOR catalyst showed a low selectivity to cracked products up to 60% of n-hexadecane conversion with product distribution close to the ideal hydrocracking regime.