The paper deals with the application of the so-called ''frameless'' T-
element approach to Poisson's equation in 2-D. The method is based on
the application of a suitably truncated T-complete set of Trefftz func
tions, over individual subdomains linked by means of a least square pr
ocedure. A specially introduced mesh consisting of elements with coeff
icients of the expansion as ''nodal'' parameters enables the assembly
of the resulting simultaneous equations to be performed, following the
rules of the usual standard direct stiffness method. The required acc
uracy of the solution can be obtained by increasing the number of eith
er elements or T-functions, which can be regarded as the h- or p-type
approach, respectively. The paper assesses convergence properties of t
he new elements, handling of patch loads, sensitivity to mesh distorti
on and possibilities of stronger enforcing continuity in displacements
or derivatives.