We prove a sharp upper bound for the resurgence of sums of ideals involving disjoint sets of variables, strengthening work of Bisui–Hà–Jayanthan–Thomas [Collect. Math. 72 (2021), pp. 605–614]. Complete solutions are delivered for two conjectures proposed by these authors. For given real numbers
a
a
and
b
b
, we consider the set
R
e
s
(
a
,
b
)
Res(a,b)
of possible values of the resurgence of
I
+
J
I+J
where
I
I
and
J
J
are ideals in disjoint sets of variables having resurgence
a
a
and
b
b
, respectively. Some questions and partial results about
R
e
s
(
a
,
b
)
Res(a,b)
are discussed.