Smoking articles, filters, and methods for selectively removing selected components from tobacco smoke are disclosed. The smoking articles and filters include composites composed of a porous alumina and/or aluminosilicate matrix containing particles of activated carbon and zeolite molecular sieve adsorbents distributed throughout the matrix which can selectively remove selected components of tobacco smoke. The composites may be made by admixing the adsorbent mixture and a binder such as aluminum hydroxide or montmorillonite clay, adding an aqueous mineral acid to gel the mixture and drying and firing the gel paste. The proportions and adsorption capacities of the components can be selected to tailor the adsorption characteristics of the composites to selectively remove targeted constituents such as acrolein and 1,3-butadiene in tobacco smoke. Methods for making filters and smoking articles using the composites, as well as methods for smoking products comprising the composites, are also provided.