  We further develop a forcing notion known as Coding with Perfect Trees and
show that this poset preserves, in a strong sense, definable $P$-points,
definable tight MAD families and definable selective independent families. As a
result, we obtain a model in which
$\mathfrak{a}=\mathfrak{u}=\mathfrak{i}=\aleph_1<2^{\aleph_0}=\aleph_2$, each
of $\mathfrak{a}$, $\mathfrak{u}$, $\mathfrak{i}$ has a $\Pi^1_1$ witness and
there is a $\Delta^1_3$ well-order of the reals. Note that both the complexity
of the witnesses of the above combinatorial cardinal characteristics, as well
as the complexity of the well-order are optimal. In addition, we show that the
existence of a $\Delta^1_3$ well-order of the reals is consistent with
$\mathfrak{c}=\aleph_2$ and each of the following:
$\mathfrak{a}=\mathfrak{u}<\mathfrak{i}$,
$\mathfrak{a}=\mathfrak{i}<\mathfrak{u}$,
$\mathfrak{a}<\mathfrak{u}=\mathfrak{i}$, where the smaller cardinal
characteristics have co-analytic witnesses.
  Our methods allow the preservation of only sufficiently definable witnesses,
which significantly differs from other preservation results of this type.
