Tear-open pouches having a first panel and a second panel sealed to one another at a non-peelable or peelable perimeter seal defining a compartment having a first compartment area of the first panel and a second compartment area of the second panel with a score disposed on the first panel extending from a first position in the perimeter seal along a first direction that extends across the first panel and into the first compartment area. An optional second score can be disposed on the first or second panel and extend from a second position in the perimeter seal along a second direction that extends across the first or second panel and into the first or second compartment area and the second position can be adjacent to the first position, and the first and second directions can be divergent to one another.