We present measurements of the field and temperature dependence of the pene
tration depth (lambda) in high purity, untwinned single crystals of YBa2Cu3
O6.95 in all three crystallographic directions. The temperature dependence
of lambda is linear down to low temperatures, showing that our crystals are
extremely clean. Both the magnitude and temperature dependence of the fiel
d dependent correction to lambda, however, are considerably different from
that predicted from the theory of the nonlinear Meissner effect for a d-wav
e superconductor (Yip-Sauls theory). Our results suggest that the Yip-Sauls
effect is either absent or is unobservably small in the Meissner state of
YBa2Cu3O6.95.