The washer leaks when it enters the spin cycle - just a little leak - water connections are tight

You need to raise the top and look around the tub to find where it is leaking. Usually you can see a trail of dried soap that will show where the leak is located. I would think a leak at a hose connection would be the most common cause. Here is a manual: https://dl.dropbox.com/u/8010163/Kenmore_Elite_Calypso%20Washing_Machine.pdf