This work presents three examples of standard test configurations, involving composite materials, where the presence of stress singularities induced by adhesive joints causes premature failures leading to underestimated strength values. Slight modifications of the local geometry, removing or reducing, in these critical points, the order of the stress singularities, have shown to give higher experimental failure loads, with almost double failure loads in the most striking cases.The three examples analyzed in the present work are: a) the tensile and shear strength determination of a bimaterial interface, b) the off-axis tension test, for the intralaminar shear strength of unidirectional long fibre composite materials and c) the compression test of thick composite laminates. In two of the three cases, the premature failure occurs at the corner where the tab (which is necessary for the grip jaw faces of the testing machine) is bonded to the composite laminate, while in the third one the failure occurs at the bimaterial interface of the two materials, all of them involving an adhesively bonded joint and corner configurations with stress singularities.With the use of a semi-analytical tool, developed by the authors, to calculate the order of stress singularities, slight and very local geometrical modifications have been successfully carried out to eliminate the stress singularity configuration. After the modifications, higher failure loads have been obtained in the tests carried out.The major outcome of the present work is the role that the singular stresses play in the premature failure of standard tests involving adhesive bonding. A correlation between the removal of the singularity stress configuration in critical parts of the samples and a higher experimental failure load, in all studied cases, has been clearly shown.