Preheat oven to 350 degrees
In a medium bowl, mix the flour and 1/4 cup of the confectioners' sugar.
Add the butter and using your hands, a pastry cutter, or two knives, mix well until the butter breaks down into s mall pealike shapes.
Press the crust into the bottom and 1/2 inch up the sides of an 8x8x2 inch baking pan or rectangular tart pan with removable bottom.
Bake on the middle rack in oven for 20 minutes.
Meanwhile, in a large bowl, beat the eggs, with a whisk or electric mixer.
Slowly add the granulated sugar, baking powder, salt, lemon peel, and lemon juice, and beat until light and fluffy, about 5 minutes.
Remove the crust from the oven.
Pour the lemon mixture over the crust.
Bake for another 15 minutes on the middle rack.
Scatter the berries over the lemon mixture and bake another 10 minutes or so. If the tart begins to brown, cover very loosely with a sheet of aluminum foil. The tart is done with a toothpick inserted in the center comes out clean.
Remove from oven and let cool.
Sift remaining confectioners' sugar on top.