For every homogeneous ideal
I
I
in a polynomial ring
R
R
and for every
p
≤
dim
R
p\leq \dim R
we consider the Koszul homology
H
i
(
p
,
R
/
I
)
H_i(p,R/I)
with respect to a sequence of
p
p
of generic linear forms. The Koszul-Betti number
β
i
j
p
(
R
/
I
)
\beta _{ijp}(R/I)
is, by definition, the dimension of the degree
j
j
part of
H
i
(
p
,
R
/
I
)
H_i(p,R/I)
. In characteristic
0
0
, we show that the Koszul-Betti numbers of any ideal
I
I
are bounded above by those of the gin-revlex
G
i
n
(
I
)
\mathrm {Gin}(I)
of
I
I
and also by those of the Lex-segment
L
e
x
(
I
)
\mathrm {Lex}(I)
of
I
I
. We show that
β
i
j
p
(
R
/
I
)
=
β
i
j
p
(
R
/
G
i
n
(
I
)
)
\beta _{ijp}(R/I)=\beta _{ijp}(R/\mathrm {Gin}(I))
iff
I
I
is componentwise linear and that and
β
i
j
p
(
R
/
I
)
=
β
i
j
p
(
R
/
L
e
x
(
I
)
)
\beta _{ijp}(R/I)=\beta _{ijp}(R/\mathrm {Lex}(I))
iff
I
I
is Gotzmann. We also investigate the set
G
i
n
s
(
I
)
\mathrm {Gins}(I)
of all the gin of
I
I
and show that the Koszul-Betti numbers of any ideal in
G
i
n
s
(
I
)
\mathrm {Gins}(I)
are bounded below by those of the gin-revlex of
I
I
. On the other hand, we present examples showing that in general there is no
J
J
is
G
i
n
s
(
I
)
\mathrm {Gins}(I)
such that the Koszul-Betti numbers of any ideal in
G
i
n
s
(
I
)
\mathrm {Gins}(I)
are bounded above by those of
J
J
.