We present a new Neumann-Neumann type preconditioner of large scale linear systems arising from plate and shell problems. The advantage of the new method is a smaller coarse space than those of earlier method of the authors; this improves parallel scalability. A new abstract framework for Neumann-Neumann preconditioners is used to prove almost optimal convergence properties of the method. The convergence estimates are independent of the number of subdomains, coefficient jumps between subdomains, and depend only polylogarithmically on the number of elements per subdomain. We formulate and prove an approximate parametric variational principle for ReissnerMindlin elements as the plate thickness approaches zero, which makes the results applicable to a large class of non-locking elements in everyday engineering use. The theoretical results are confirmed by computational experiments on model problems as well as examples from real world engineering practice.