Cream together the butter or margarine and 3/4 cup sugar. Beat until light and fluffy. Separate the eggs. Beat in the egg yolks one at a time, and add the key lime zest.
Sift together the flour, baking powder, baking soda, and salt.
Add these dry ingredients to the egg butter mixture, alternating with 1/2 cup key lime juice.
Beat the egg whites until stiff, and fold into the batter.
Pour batter into a well greased 10 inch Bundt pan.
Bake for 30 to 35 minutes at 350 degrees F (175 degrees C), or until cake tests done. Cool cake for 10 minutes in pan, and then invert onto cooling rack.
Combine 1/4 cup sugar and 1/4 cup key lime juice. Simmer over medium low heat until a light syrup forms; this should take approximately 5 minutes. Use glaze immediately.