Euclidean distance layer truncated for points at edge.

Hello,

I need to find euclidean distance from multiple points. I reprojected the layer from GCS-1983 to NAD_1983 before running the euclidean distance tool. Euclidean distance layer is truncated for points at edge; not extending beyond northernmost, westernmost (etc) points. It appears there is a rectangle that barely includes the furthest points. I think this in related to the extent of the point layer. As I write this it occurs to me to add spurious points further out to increase the extent of the layer and then re-project it. . . seems kludgy; there must be a better solution. Any ideas?

Thanks!

Paul