NOVELTY - Nucleic acid construct comprising a regulatory element and a Fat B gene expressing an active acyl-acyl-acyl carrier protein thioesterase operable to produce an altered fatty acid profile in an oil produced by a cell expressing the nucleic acid construct is new, where the Fat B gene expresses a protein having an amino acid sequence as given in clade 5 of table 1a or clades 1-12 of table 1a of the specification.    USE - The nucleic acid construct is useful for producing an oil or oil-derived product (claimed), where the oil is used to produce foods, oleochemicals, fuels and chemicals including plastics, foams, and films.    DETAILED DESCRIPTION - Nucleic acid construct comprising a regulatory element and a Fat B gene expressing an active acyl-acyl-acyl carrier protein thioesterase operable to produce an altered fatty acid profile in an oil produced by a cell expressing the nucleic acid construct is new, where the Fat B gene expresses a protein having an amino acid sequence as given in clade 5 of table 1a or clades 1-12 of table 1a of the specification, and the sequence has at least 94.6% sequence identity with each of SEQ ID NOs: 88 and 85 (each comprising a fully defined sequence of 415 amino acids as given in the specification), SEQ ID NO: 82 (comprising a fully defined sequence of 414 amino acids as given in the specification), and SEQ ID NO: 103 (comprising a fully defined sequence of 393 amino acids as given in the specification), and optionally the fatty acid of the oil is enriched in 8-10C fatty acids. INDEPENDENT CLAIMS are also included for:    (1) an isolated nucleic acid or recombinant DNA construct comprising a nucleic acid, where the nucleic acid has at least 70% sequence identity to any one of SEQ ID NOs: 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 76, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102, 104, 105, 107, or 109 (comprising fully defined sequences of 1074-1284 nucleotides as given in the specification) or any equivalent sequences by virtue of the degeneracy of the genetic code;    (2) an isolated nucleic acid sequence encoding a protein or a host cell expressing a protein having at least 70% sequence identity to any of SEQ ID NOs: 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 75, 77, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 108, or 110-192 (comprising fully defined sequences of 355-428 amino acids as given in the specification) or its fragment having acyl-acyl-acyl carrier protein thioesterase activity;    (3) producing (M1) a recombinant cell that produces an altered fatty acid profile, comprising transforming the cell with the nucleic acid;    (4) a host cell produced by the method (M1);    (5) producing (M2) an oil or oil-derived product, comprising cultivating the host cell, and extracting oil produced from it, optionally where the cultivation is heterotrophic growth on sugar;    (6) an oil produced by the method (M2), optionally having a fatty acid profile comprising at least 20% 8C, 10C, 12C, 14C or 16C fatty acids; and    (7) an oil-derived product produced by the method (M2).