Leaking toilet question....

My toilet was leaking around the flapper. I confirmed this by putting a few drops of food coloring in the tank and the bowl water would turn color.
I replaced the flapper with a FloMaster Bulls Eye and the leak stopped. I confirmed this with the food dye test.

Now, to my problem.
With the old flapper, when you flushed the toilet only about 1/2 of the tank would empty. This was sufficient for most uses of the toilet. If you needed a full flush all you needed to do was to hold the handle down to completely drain the tank.
This was a nice set-up because the majority of the time it wouldn't drain the tank....thereby saving water but still flushing enough to clean the bowl.

But now, after installing the new flapper, a regular push of the handle drains the tank almost completely.

Does anyone have any idea why the toilet is flushing different with the new flapper? Do i need to adjust the chain that connects the flapper to the handle?

I would like to get the toilet back to its old ways, just without the leaky flapper.

Thanks.

http://www.korky.com/Flapper16BP.html

They make replacement 1.6 flappers. Korky is one brand I use that should be on the hardware shelf.
Just make sure it's marked for 1.6 gallons.

http://www.korky.com/Flapper2004BP.html

Some flappers come with a little styrofoam ball that you can move up and down the chain to adjust the flush volume.