Spray a 15 x 10 x 1 in. (37 x 25 x 3 cm) jelly-roll pan; line the bottom with waxed paper; spray the paper.
Sift the flour and baking powder together.
With an electric mixer, beat the eggs in a medium bowl until thick and creamy and light in color.
Gradually add the sugar and the acesulfame-K, beating constantly until the mixture is very thick.
Stir in the water and vanilla.
Fold in the flour mixture.
Spread the batter evenly in the prepared pan.
Bake at 375°F (190°C) for 12 minutes or until the center of the cake springs back when lightly pressed.
Loosen the cake around the edges with a knife.
Invert the pan onto a clear tea towel, and peel off the waxed paper.
Starting at the short end, roll up the cake and towel together.
Place the roll seam-side-down on a wire rack and cool completely.
When cool unroll carefully and assemble with filling.
With a sharp knife, score the places where the slices will be, so they are even.