NOVELTY - Mutant thioesterase derived from a precursor thioesterase, where the mutant has at least one altered property in vitro and/or in vivo as compared to the precursor thioesterase, is new.    USE - The mutant thioesterase is useful for: producing a fatty acid derivative; producing a fatty acid derivative extracellularly, where the fatty acid derivative is a modified fatty acid derivative, or is (or a component of) a fuel, fuel additive, fuel blend, detergent, surfactant, nutritional supplement, polymer, paraffin replacement, lubricant, solvent, personal care product, rubber processing additive, corrosion inhibitor, emulsifier, plastic, textile, cosmetic, paper product, coating, metalworking fluid, dielectric, oiling agent, or emollient; and producing a biofuel or a fuel composition (all claimed).    ADVANTAGE - The mutant thioesterase permits production of fatty acid derivative compositions whose properties can be tailored to suit specific purposes e.g. a composition with improved fuel characteristics e.g. cloud point.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for:    (1) a polynucleotide (Ia) encoding the mutant thioesterase or its naturally-occurring equivalent;    (2) a vector comprising (Ia);    (3) a recombinant host cell (B1) comprising (Ia) or the vector;    (4) a recombinant cell (B2) comprising (Ia) or the vector, where at least one of the genes acyl-coenzyme A dehydrogenase (fadE), NADPH-dependent glycerol-3-phosphate dehydrogenase (gpsA), lactate dehydrogenase A (ldhA), pyruvate-formate lyase (pflB), phosphotransacetylase (pta), pyruvate oxidase (poxB), acetate kinase A (ackA), acetate kinase B (ackB), glycerol-3-phosphate acyltransferase (plsB) and/or sfa is attenuated;    (5) a recombinant cell (B3) comprising (Ia) or the vector, and at least one polynucleotide encoding at least one fatty acid derivative enzyme;    (6) a recombinant cell (B4) comprising (Ia) or the vector, and at least one polypeptide encoding at least one acyl-Coenzyme A (CoA) synthase enzyme, which is long chain acyl-CoA synthetase (fadD), short chain acyl-CoA synthetase (fadK), BH3102, acyl-CoA synthetase yhfL, Pfl-4354, EAV15023, fadD1, fadD2, acyl-CoA synthetase RPC4074, fadDD35, fadDD22, faa3, and/or the gene encoding a protein of GenBank accession number ZP 01644857;    (7) a recombinant cell (B5) comprising (Ia) or the vector, and at least one polynucleotide encoding at least one ester synthase, at least one fatty aldehyde biosynthetic enzyme, at least one fatty alcohol production gene or at least one olefin producing gene;    (8) a recombinant cell (B6) comprising (Ia) or the vector, where at least one gene encoding acyl-CoA dehydrogenase enzyme is attenuated or deleted;    (9) a method of producing a fatty acid derivative comprising cultivating (B1)-(B6) under conditions that permit the production of a fatty acid derivative;    (10) a method of producing a fatty acid derivative extracellularly comprising growing (B1)-(B6) under conditions that permit the expression of the mutant thioesterase or its naturally-occurring equivalent, harvesting the cell, lysing the cell and providing a substrate to the cell lysate under conditions that permit the production of the fatty acid derivative;    (11) a fatty acid derivative produced by the methods;    (12) a biofuel composition comprising at least one fatty acid derivative; and    (13) a fuel composition comprising the biofuel composition.