Electrical connectors are provided with spring contact elements (220f) each having a tapered contact portion (221) for mating with the plated rim of a hole. The tapered contact portion can be configured as a bifurcated cone, a suitably shaped wire (421), or other tapered, flexible contact. Besides the contact portion, the contact elements also include spring portions (236f), which can assume various configurations and tail portions (323) which can also assume various configurations. Where the tapered contact portion is a suitably shaped wire (421), the spring portion and the contact portion are essentially the same. The tail portions can be arranged to have tapered contact portions where permanent connection of the tail is not desired. The disclosed electrical connectors have housings (230) for the spring contact elements (220f), and a first make, last break function can be provided by configuring the housings appropriately. The holes with which the tapered spring contact elements mate can be part of a printed circuit board (250), a flex circuit (350h), or other object.