We have analyzed the electromagnetic properties of small and long YBa 2 Cu 3 O 7Ϫx grain-boundary Josephson junctions. The Swihart velocity increases with junction width ͑w͒ while the ratio of the relative dielectric constant to the barrier thickness (/t) decreases. We found that the product wϫ/t is approximately constant. These results have been explained in the framework of the filamentary model, where the barrier can be regarded as a disordered dielectric medium with a high density of superconducting filaments. Experiments demonstrate that a controllable variation of these parameters can be achieved by helium irradiation at 80 keV. We give examples of an enhancement of weak-link properties of junctions for doses in the range of 10 13 cm Ϫ2. Raising the dose we can sweep the modification of the weak-link properties from an increase of the junction critical current of about 10% to a severe degradation of the coupling energy of the barrier, although the superconducting properties of the electrodes always worsen gradually.