Put them in the washer
... Just kidding
MSPaint will do the job but at the cost of heavy compression to quality.
Thats how I do. Some of my pics turn out to be 1.1MB or so after editing (at 1500px wide). I use quality setting as 11 and works great with no visible quality degradation.
By the way, what size do you trying to submit? Usually JPG's with 1000px wide don't usually cross the 1Mb mark unless the picture contains a lot of details and colors...