This paper uses DFT and G3(MP2) calculations to examine whether unbridged 10-membered rings can be made by (pi)6 + (pi)4 cycloadditions to (Z)- and (E)-hexatrienes, hexa-1,5-dien-3-ynes, (Z)-hexa-1,3-dien-5-ynes, hexa-1,2,3,5-tetraenes, and (Z)-hexa-3-ene-1,5-diynes. Cycloadditions to four 4 pi reactants, buta-1,3-diene, butenyne, butatriene, and butadiyne, are explored. Thirty different basic cycloadditions are identified, and all are shown to be exothermic according to G3(MP2) calculations; strain energies in the products are comparable with that of cyclodecane itself, despite the presence of trans-alkene, alkyne, allene, cumulene, and s-trans diene moieties. The major obstacles to the isolation of 6 + 4 cycloaddition products are competing (pi)4 + (pi)2 cycloadditions and, especially, rapid Cope rearrangement of the products, but, in many cases, the judicious introduction of substituents can overcome these problems so that practical syntheses should be possible. Reactions between (E)-hexa-1,3,5-triene and s-trans-buta-1,3-diene are shown to have substantially lower activation energies than those involving (Z)-hexa-1,3,5-triene reacting with either s-cis- or s-trans-buta-1,3-diene. Conformationally locked derivatives of s-cis,s-cis (E)-hexa-1,3,5-trienes can lead to derivatives of (Z,Z,E)-cyclodeca-1,3,7-triene that are stable to Cope rearrangement, and reactions should proceed at close to ambient temperatures with suitable activating groups. We predict that it should be possible to prepare suitably substituted derivatives of at least 11 more highly unsaturated ring systems: (5Z,7Z)-cyclodeca-1,2,5,7-tetraene,(1 Z,32)-cyclodeca-1,3-dien-7-yne, (2Z,7E)-cyclodeca-1,2,3,7-tetraene, (Z)-cyclodeca-1,2,3-trien-7-yne, (4Z,8E)-cyclodeca-1,2,4,8-tetraene, (Z)-cyclodeca-1,2,4,5,7-pentaene, (2)-cyclodeca-1,2,4-trien-8-yne, (1Z,7E)-cyclodeca-1,7-dien-3-yne, (R,S,E)-cyclodeca-1,2,4,5,8-pentaene, cyclodeca-1,2,4,5,8,9-hexaene, and (R,S)-cyclodeca-1,2,4,5-tetraen-8-yne. In three other cases, we predict that cycloaddition will be followed by unusual and intriguing rearrangements. Cycloadditions can be accelerated by the presence of electron-withdrawing groups in either the 6 pi or 4 pi reactants. Transannular cyclizations of some products may lead to interesting stereocontrolled routes to 6,6- and/or 5,7-bicyclic structures.