Prism99

You can prevent this problem by measuring your quilt top through the middle. Cut two of your border strips to that measurement, then pin the strips to the quilt top before sewing, pinning the middles together first, then the ends, and then as many pins as needed in-between. Once those two borders are sewn and ironed on, measure your quilt through the middle in the other direction to figure out how long to cut the remaining two border strips. (An easy way to cut these strips is to fold your quilt in half, then lay your strip along that fold and cut.) The reason for doing this is to make sure that your border strips on both sides are equal (necessary in order to have a squared finished quilt), and also to make sure that you are not sewing excess border fabric onto the quilt top.

What happens when you simply sew border strip to top without first measuring and cutting to size is that the simple act of sewing tends to stretch either the border fabric or the top, or both. This is not obvious on small pieces of fabric when you are sewing blocks together, but it adds up when you are sewing a single long strip -- especially when the quilt top's edge has many seams in it.

Cutting the border strips on the lengthwise grain of the fabric (parallel to the selvedges) can also help as fabric does not stretch as much on this grain as it does on the crosswise grain (width of fabric). However, you still need to pre-measure and pre-cut the border strips because the quilt top edges themselves can be stretching. Measuring through the quilt top's middle and cutting the border strips to that measurement ensures that, if the quilt top's edges have stretched with handling, you will know when pinning that you need to ease in that quilt top edge.

In terms of a solution, if your border fabric is a plain fabric, your best bet is to run machine gathering stitches (basting stitches) around each edge. Gather up the excess until the edge measurement matches the top measurement. Secure the ends and distribute the gathers evenly, then machine baste the quilt top edge to the other two layers before binding. (You can sew the binding on before trimming the edges so that you don't accidentally cut through your gathering stitches.)

If your border fabric is patterned, you can make some darts from the outer edge towards the inner. Many patterns, especially smaller ones, will render these darts almost invisible.