We describe a new approach for the finite-element modelling of strain-gradient models with a mixed formulation. This approach uses degrees of freedom shared between the displacement and displacement-gradient fields. This results into elements which have fewer degrees of freedom, without the disadvantage of reducing the interpolation order for the displacement field. Testing shows that these elements can deliver a significantly improved numerical performance compared to existing elements. We present the general approach of the method, and how this leads to a family of similar finite elements. The elements have a relatively simple formulation, which can be conveniently expressed within a standard framework. They can therefore easily be implemented in existing finite element codes, although the formulation leads to mid-side nodes having coordinates to describe geometry, but having no associated degrees of freedom. The formulation can be further simplified, reducing the number of degrees of freedom, by introducing a penalty formulation instead of Lagrange multipliers. In this case, however, a robust method for determining the penalty parameter is then required. The applicability of the approach to three-dimensional elements is also discussed.