  Weak scale supersymmetry is often said to be fine-tuned, especially if the
matter content is minimal. This is not true if there is a large A term for the
top squarks. We present a systematic study on fine-tuning in minimal
supersymmetric theories and identify low energy spectra that do not lead to
severe fine-tuning. Characteristic features of these spectra are: a large A
term for the top squarks, small top squark masses, moderately large tan\beta,
and a small \mu parameter. There are classes of theories leading to these
features, which are discussed. In one class, which allows a complete
elimination of fine-tuning, the Higgsinos are the lightest among all the
superpartners of the standard model particles, leading to three nearly
degenerate neutralino/chargino states. This gives interesting signals at the
LHC -- the dilepton invariant mass distribution has a very small endpoint and
shows a particular shape determined by the Higgsino nature of the two lightest
neutralinos. We demonstrate that these signals are indeed useful in realistic
analyses by performing Monte Carlo simulations, including detector simulations
and background estimations. We also present a method that allows the
determination of all the relevant superparticle masses without using input from
particular models, despite the limited kinematical information due to short
cascades. This allows us to test various possible models, which is demonstrated
in the case of a model with mixed moduli-anomaly mediation. We also give a
simple derivation of special renormalization group properties associated with
moduli mediated supersymmetry breaking, which are relevant in a model without
fine-tuning.
