I agree, Cross midfield at pattern altitude, and enter down wind. give
way to aircraft entering on the 45. The reason for instructors
teaching the crossing at 500-1000' over and then entering the 45 is a
because that is the recommended proceedure in the AIM. This is one
area that I think the AIM is lacking in that I can not come up with any
good reason to do this over the cleaner shorter and aurguably safer
method of crossing at pattern altitude and just turning downwind. I
really like the AOPA Air Safety Foundation document on flying and
Non-towered airports. I just wish they could get the FAA to go along
with (and provide FAA documentation) supporting the Alternate pattern
entry they show. Perhaps more instructors would start teaching the
alternate method which I believe is safer.

(My Safer aurgment goes like this: Against overflying and enter on the
45. 1. flying over the pattern it is very difficult to see aircraft
below you in the ground clutter. 2. How far out do you go to get out of
the pattern to descend to pattern altitude. I watch twins routinely fly
3 mile patterns, This is nearly a Cross Country in the J-4. 3.
Skydivers and Turbine aircraft patterns are routinely at the 1500 to
2000' level. 4. above 1000' it is much more difficult to see Windsocks
and other details about the runway. For overfly at Pattern altitude.
1. Efficent 2. Never leave gliding range of the runway 3. Can see other
aircraft better since they should all be at pattern altitude. 4. Can
See windsock and other runway details better.

Brian