This study presents a mathematical background that justifies a new use of Laplace space in well-test analysis. It enables us to perform the whole parameter identification (C(D), S, k, h, etc.) in Laplace space or at least gives us a powerful tool to treat pressure data to recognize the model to use for parameter identification in real space. It shows how the Laplace transform of pressure can be plotted with exactly the same behavior as the real pressure function so that the plots keep their familiar shape. The coefficients of the dimensionless parameters also remain the same, which enables us to display a new set of characteristic and easily understandable type curves in Laplace space. The mathematical background also sheds light on use of the Laplace transform to deconvolute flow rates by modifications of earlier techniques that were extremely sensitive to noise in the data. The Laplace-space approach provides an entirely new way of examining and understanding well-test results. It has been applied successfully to noisy, simulated data and real field data where conventional interpretation could not illuminate ambiguities.