The settlement estimation of a shallow foundation requires the laboratory determination of the soil modulus or the compression index by oedometer or triaxial tests. The oedometer soil samples, by whose testing the two indices are determined, present a certain disturbance during their extraction from the ground and sampler tube respectively. This fact, together with setting the samples to a stress/strain state different from the in situ ones, determines a deviation of the results from reality. The authors designed a new oedometer device, to decrease or eliminate the induced testing errors, that differs from the classical one by the followings: the test is performed directly on the soil specimen removed from the boreholes without sampling the 70 mm diameter and 20 mm height cylinders; the stress-strain and stress-voids ratio curves, to determine these two indices, are obtained on samples with a partial lateral confined strain, under a stress state close to the one in situ; the new oedometer device provides the condition to perform a plate load test and obtain the stress-settlement curve, based on which the vertical subgrade modulus and by correlation the soil modulus can be derived. Thus, the paper presents the general approach to perform these two types of tests and their corresponding individual stages to quantitatively assess the soil compressibility by the soil modulus and compression index, established for pre-existing and induced stress states as similar as possible to the in situ ones, before and after construction is performed.