B-physics is currently facing a number of puzzles, and additional precision data - and precision calculations - will be required to pick these apart. In particular, as the Belle II detector approaches completion, there is increasing need for lattice calculations related to CKM matrix elements and to important B branching ratios such as $\mathcal{B} (B \rightarrow \tau \nu)$.

We present early results for $f_B$ and $f_{B_s}$ from the CSSM/QCDSF/UKQCD collaboration on a set of lattices with a fixed volume $32^3\times64$ and lattice spacing $a=0.074$~fm. By varying the $u$,$d$,$s$ quark masses while holding their average value constant, we are able to reliably control the SU(3)-flavour breaking effects.