Dice tomatoes. If using cherry tomatoes cut them into quarters lengthwise, then crosswise, into 8 pieces. Place in medium bowl.
Finely dice white onion, place in bowl with tomatoes.
Cut ends off of the jalapeno peppers. Slice the peppers into quarters lengthwise, then, using a paring knife, slice away the internal membranes and seeds. Slice pepper quarters into long narrow strips, and then cut strips crosswise into very small dice. Add to bowl.
Remove clean cilantro leaves from stems, and finely mince. Add to bowl.
Juice the lime half into the vegetables in the bowl. Add about 1 teaspoon of salt, stir together. Taste.
Let the mixture sit a while before eating, to give the flavors a chance to meld. Keep covered in the fridge; use within 5 days.