  We study fair division of indivisible chores among $n$ agents with additive
disutility functions. Two well-studied fairness notions for indivisible items
are envy-freeness up to one/any item (EF1/EFX) and the standard notion of
economic efficiency is Pareto optimality (PO). There is a noticeable gap
between the results known for both EF1 and EFX in the goods and chores
settings. The case of chores turns out to be much more challenging. We reduce
this gap by providing slightly relaxed versions of the known results on goods
for the chores setting. Interestingly, our algorithms run in polynomial time,
unlike their analogous versions in the goods setting.
  We introduce the concept of $k$ surplus which means that up to $k$ more
chores are allocated to the agents and each of them is a copy of an original
chore. We present a polynomial-time algorithm which gives EF1 and PO
allocations with $(n-1)$ surplus.
  We relax the notion of EFX slightly and define tEFX which requires that the
envy from agent $i$ to agent $j$ is removed upon the transfer of any chore from
the $i$'s bundle to $j$'s bundle. We give a polynomial-time algorithm that in
the chores case for $3$ agents returns an allocation which is either
proportional or tEFX. Note that proportionality is a very strong criterion in
the case of indivisible items, and hence both notions we guarantee are
desirable.
