You have the easier situation, you want the T phenotype in your variety's background that has the genotype tt. So you can raise the F1 and all should have the T phenotype. Depending on the breeding system of your crop, you may need to alter the following. If your crop tolerates inbreeding well and your variety tt is relatively inbred, just keep backcrossing the resulting progeny possessing the T trait to your tt parent until you have something that looks like your tt parent with the T phenotype. Through backcrossing like this repeatedly, the progeny you obtain with the T phenotype will have a Tt genotype. If it is a seed strain you are raising (not an asexually propagated crop where you can just clone a favorable individual), you will then want to do a generation of selfing with the Tt plants that look like tt, but with the T phenotype. Then from those plants you will have some that have the genotypes with TT, Tt and tt. Self the plants with the T phenotype to see which produce 100% T phenotype offspring and then you identified the TT genotypes. From then on you can self those plants and hopefully reliably produce what you want from seed. This is done routinely for soybeans bringing in the Roundup ready gene to different lines and the same for inbred corn lines for that same gene as well as others like Bt.

Sincerely,
David

Thank you David. I'm actually talking about peas which are inbreeders. When you say repeated backcrossing how many generations would be necessary do you think? It's actually 3 genes, all dominant, that I want to introduce but the characteristic I'm looking for doesn't show up in the phenotype unless all 3 are present, or so I believe. In other words, if the 3 are A, B and C then the phenotype A_B_C_ will show the trait I'm after but not A_B_cc for example.

Interesting!

So in your F1 you should have all Aa Bb Cb possessing the trait. In your backcross only .5 (probability of A) times .5 (B)times .5 (C) or one out of 8 seedlings should have the trait, assuming all three genes segregate independantly and are not linked. Number of backcrosses is hard to say depending on the inheritance of the traits you really want from your aa bb cc parent. The last step of selfing to get AA BB CC homozygous will take more generations because all three need to be homozygous, but it can be done.

Good Luck!

David