Synapses that can be strengthened in temporary and persistent manners by two separate mechanisms are shown to have powerful advantages in neural networks that perform auto-associative recall and recognition. A multiplicative relation between the two weights allows the same set of connections to be used in a closely interactive way for short-term and long-term memory Algorithms and simulations are described for the storage, consolidation and recall of patterns that have been presented only once to a network. With double modifiability, the short-term performance is dramatically improved. becoming almost independent of the amount of long-term experience. The high quality of short-term recall allows consolidation to take place. with benefits from the selection and optimization of long term engrams to take account of relations between stored patterns. Long-term capacity is greater than short-term capacity. with little or no deficit compared with that obtained with singly modifiable synapses. Long-term recall requires special. simply implemented. procedures for increasing the temporary weights of the synapses being used to initiate recall. A consolidation algorithm is described for improving long-term recall when there is overlap between patterns. Confusional errors are reduced by strengthening the associations between non-overlapping elements in the patterns, in a two-stage process that has several of the characteristics of sleep.