The authors present general results for finding or bounding 
, the maximum number of arbitrary whole blocks of observations which can be removed from a block design, and still leave all of the elementary treatment contrasts estimable. The block sizes may be larger than the number of treatments. The results are applied to BBDs, reinforced BIBDs and BBDs, BTIBDs, and a series of variance balanced incomplete block designs with two block sizes. Also given for most of these designs, are results for 
the maximum number of arbitrary, scattered observations that can become unavailable, and still leave all of the elementary treatment contrasts estimable.
