For a Noetherian local ring
(
R
,
m
)
(\mathbf {R}, \mathfrak {m})
, the first two Hilbert coefficients,
e
0
e_0
and
e
1
e_1
, of the
I
I
-adic filtration of an
m
\mathfrak {m}
-primary ideal
I
I
are known to code for properties of
R
\mathbf {R}
, of the blowup of
Spec
(
R
)
\operatorname {Spec}(\mathbf {R})
along
V
(
I
)
V(I)
, and even of their normalizations. We give estimations for these coefficients when
I
I
is enlarged (in the case of
e
1
e_1
in the same integral closure class) for general Noetherian local rings.