VolvoGirl, that is incorrect. They are definitely mandatory if you expect to owe $1000 or more in taxes on the amount of self employment income for the year. If you do not pay enough quarterly tax in, you may be penalized if the amount you still owe at tax time for self-employment income is $1000 or more.
If you have already made two quarterly payments, and now expect that your estimated quarterly tax should be Zero for the next two quarters, then the IRS website says to complete a new 1040-ES worksheet for your records to show the new figure. Anytime you need to amend the quarterly amount, you do a new worksheet for the new quarter. I urge you to go to the IRS website and open "Form 1040-ES" and read the first page of that publication.
