  The measured $\bar{B}\to D^{(*)} l \bar\nu$ decay rates for light leptons
($l=e,\mu$) constrain all $\bar{B}\to D^{(*)}$ semileptonic form factors, by
including both the leading and ${\cal O}(\Lambda_{\text{QCD}}/m_{c,b})$
subleading Isgur-Wise functions in the heavy quark effective theory. We perform
a novel combined fit to the $\bar{B}\to D^{(*)} l \bar\nu$ decay distributions
to predict the $\bar{B} \to D^{(*)} \tau\bar\nu$ rates and determine the CKM
matrix element $|V_{cb}|$. Most theoretical and experimental papers have
neglected uncertainties in the predictions for form factor ratios at order
$\Lambda_{\text{QCD}}/m_{c,b}$, which we include. We also calculate ${\cal
O}(\Lambda_{\text{QCD}}/m_{c,b})$ and ${\cal O}(\alpha_s)$ contributions to
semileptonic $\bar{B}\to D^{(*)} \ell \bar\nu$ decays for all possible $b \to
c$ currents. This result has not been available for the tensor current form
factors, and for two of those, which are ${\cal
O}(\Lambda_{\text{QCD}}/m_{c,b})$, the corrections are of the same order as
approximations used in the literature. These results allow us to determine with
improved precision how new physics may affect the $\bar{B}\to D^{(*)}
\tau\bar\nu$ rates. Our predictions can be systematically improved with more
data; they need not rely on lattice QCD results, although these can be
incorporated.
