To check the shrinkage of the concrete considered for a design and construction project, only a limited time such as 1-3 months is usually available. So, a short-time shrinkage test must be extrapolated to much longer times, which has been known to be a difficult problem. To obtain a dependable extrapolation, it was proposed to use weight measurements of the water loss of the test specimens. However, recently some problems with this concept have been identified. The present article proposes another concept relying on the diffusion size effect in shrinkage. In a much smaller companion specimen, it is possible to reach within 1-3 months the concave part of the shrinkage curve plotted in logarithmic time scale, in which the asymptotic value is closely approached. The method is examined using the available published data on the shrinkage of specimens of different sizes. Because the size difference in the available data is too small, the method is also examined using artificial small-size data obtained by scaling according to the diffusion theory. Both cases indicate overall improvement in predicting the final asymptotic values. However, although the extrapolation is clearly better than the traditional extrapolation "by eye" or by fitting a formula to one-size data, some non-negligible discrepancies are still observed, and it is not clear whether the size effect method is better than the water loss method. In the face of this reality, further studies are recommended using tests of combined drying and autogenous shrinkages, with greater size differences of drying specimens and a refined evaluation taking into account secondary influences such as differences in cracking, hydration aging, and the inevitable effect of autogenous shrinkage in the specimen core before it is reached by the drying front. Until such studies clarify the problem, taking the more conservative result from the extrapolations by the size-effect and weight-loss methods is recommended as better than intuitive extrapolation "by eye".