Creating a buffer around many point features while eliminating gaps

[Theisen]

I am looking to see if there a way to create a buffer around a bunch of point features, but to eliminate gaps within the buffer. Essentially, I need to quantitatively draw a boundary around the grouping of points to create a site. Using the existing buffer tools, you can dissolve into a single buffer feature, but there are still gaps in the buffer. I know that I could make the buffer large enough to cover the extent of the point group, however, then my site would be massively inflated. I would manually draw my buffer around the points, but this is also not an option as I need to be able to explain statistically, how the buffer was generated. 

I appreciate any and all help! 

[DavidSolari]

Couple of options off the top of my head, depending on what you want the output to look like:

1. Run Minimum Bounding Geometry with a convex hull and then buffer those results.
2. Feed the buffer in Union with "Gaps Allowed" unchecked and then into Dissolve.

[DavidPike]

Ah yes I remember the old 'Union to itself hack'!  very handy unless something better has replaced it.