One of the long-standing goals in landmine and UXO detection research has been to identify metal objects based on their electromagnetic induction~(EMI) responses. An often-pursued approach is to model the time-domain response of an object with a sum of damped real exponentials whose amplitude and decay coefficients are related to the object's geometric and electromagnetic properties. Using this model, a measured response can be processed, by a number of techniques, in an attempt to extract the associated amplitude and decay coefficients of the constituent exponentials. These coefficients can be potentially related to the object's physical properties. Some years ago the authors investigated this approach using computer simulated data with added noise. Even for the simple case of a sphere, it was not possible to reliably and uniquely estimate the amplitudes and decay constants, particularly in the absence of some a priori information about the object. The basic problem is that damped real exponentials are highly correlated functions. That is, while it is easy to fit a response with a sum of these exponentials, the accuracy of the estimate of their parameters (amplitude and decay constants) is not guaranteed, making it difficult to relate extracted parameters to object properties. The paper illustrates this point using the EMI response of a sphere and the characteristics of fitting exponential sums to data. For objects more complex than the sphere, there will be additional problems such as the dependence of the response on object orientation and depth. In practice, the problem will be exacerbated by low signal strength (particularly for minimum metal landmines), uncertain or unknown object location and depth and the occurrence of a large number of false targets, some of which will have responses which are statistically identical with that of the target being sought. As well, a false target in the proximity of a real target will alter or totally mask the response of the latter.