Soak the rice in cool water to cover for about 30 minutes. Drain.
While the rice is soaking, melt the butter in a medium sauté pan or skillet over low heat. Add the onions and cook, stirring occasionally, until translucent and tender, about 10 minutes. Add the garlic and cook a few minutes more. Add the rice, diced tomatoes, pine nuts, currants, parsley, mint, salt, and pepper and combine well.
Snip the stems off the grape leaves and place smooth side down on a table. Place a teaspoon or so of the rice filling near the stem end of each leaf. Fold the sides of each leaf over the filling, then roll into a cylinder. The rice expands as it cooks so do not roll too tightly.
If tomatoes are in season, line a pan large enough to fit the dolmas in a single layer with the tomato slices. Arrange the dolmas seam side down and close together on the tomato slices or on the bottom of the pan. Pour the olive oil and lemon juice over top and add enough hot water to just cover the dolmas. Weight them with a plate to keep them from unrolling.
Heat the liquid to boiling and cover the pan. Reduce the heat and simmer 35 to 40 minutes. Uncover the dolmas so that they can cool quickly. As soon as they can be handled, remove the dolmas with a spatula and arrange on a platter (see Note). Serve warm or at room temperature with lemon wedges and yogurt.