A method of increasing production of fatty acids comprising introducing into a host and expressing therein an acyl-acyl carrier protein (ACP) thioesterase (TE) from Bryantella formatexigens or a mutant thereof; a method of making a mutant B. formatexigens acyl-ACP TE; a method of making a chimeric Cuphea viscosissima acyl-ACP TE; a nucleic acid molecule comprising a nucleotide sequence encoding a mutant acyl-ACP TE or a chimeric Cuphea viscosissima acyl-ACP TE; a host comprising the nucleic acid molecule; a mutant acyl-ACP TE or chimeric Cuphea viscosissima acyl-ACP TE; a method of altering the specificity of a plant acyl-ACP TE for at least one of its substrates comprising introducing into the plant acyl-ACP TE a substrate specificity-altering mutation; and a method of altering the level of activity of a plant acyl-ACP TE.