  We devise a simple modification that essentially doubles the efficiency of a
well-known quantum key distribution scheme proposed by Bennett and Brassard
(BB84). Our scheme assigns significantly different probabilities for the
different polarization bases during both transmission and reception to reduce
the fraction of discarded data. The actual probabilities used in the scheme are
announced in public. As the number of transmitted signals increases, the
efficiency of our scheme can be made to approach 100%. An eavesdropper may try
to break such a scheme by eavesdropping mainly along the predominant basis. To
defeat such an attack, we perform a refined analysis of accepted data: Instead
of lumping all the accepted data together to estimate a single error rate, we
separate the accepted data into various subsets according to the basis employed
and estimate an error rate for each subset {\it individually}.
