  Morphic words are letter-to-letter images of fixed points $x$ of morphisms on
finite alphabets. There are situations where these letter-to-letter maps do not
occur naturally, but have to be replaced by a morphism. We call this a
decoration of $x$. Theoretically, decorations of morphic words are again
morphic words, but in several problems the idea of decorating the fixed point
of a morphism is useful. We present two of such problems. The first considers
the so called $AA$ sequences, where $\alpha$ is a quadratic irrational, $A$ is
the Beatty sequence defined by $A(n)=\lfloor \alpha n\rfloor$, and $AA$ is the
sequence $(A(A(n)))$. The second example considers homomorphic embeddings of
the Fibonacci language into the integers, which turns out to lead to
generalized Beatty sequences with terms of the form $V(n)=p\lfloor \alpha
n\rfloor+qn+r$, where $p,q$ and $r$ are integers.
