  New physics (NP) in charmless strangeness-changing $B$ and $B_s$ decays,
which are dominated by the $b \to s$ penguin amplitudes, can either preserve
isospin or change it by one unit. A general formalism is presented studying
pairs of processes related to each other by isospin reflection. We discuss
information on $\Delta I$ in NP amplitudes, provided by time-integrated
CP-violating rate asymmetries in $B^+$ and $B^0$ decays (or in $B_s$ decays),
differences between rates for isospin-reflected processes, and coefficients $S$
of $\sin \Delta m t$ in time-dependent CP asymmetries. These four asymmetries
in $B^+$ and $B^0$ decays (or five asymmetries in $B_s$ decays) are shown to
determine the magnitude and CP-violating phase of a potential isovector NP
amplitude, and the imaginary part of an isoscalar amplitude, assuming that
strong phases in NP amplitudes are negligible. This information may be compared
with predictions of specific models, for which we discuss a few examples.
