Use cases vs use case scenarios

I need to specify use cases for deleting 2 type of objects x and y, where y is a list of object x.

I want to avoid the excessive fragmentation of use cases, because the flow of event between the 2 use cases is similar.Should I specify 2 use cases, Delete x and Delete y, or a single use case Delete object with the main scenario for deleting x and an alternative scenario for delete y? Or there is a better solution? More generally, for similar cases such as for example sharing objects x and objects y, what would be the recommended approach and when to use the alternative scenarios?

Here is what I meant with the first option:

Use case Delete x

Pre-conditions: AuthenticationPost-Condition: The object x is deletedMain scenario:1.The actor starts the use case2.The system shows the list of objects x3.The actor selects the object x to delete4.The system deletes the object x

Use case Delete y

Pre-conditions: AuthenticationPost-Condition: The object y is deletedMain scenario:1.The actor starts the use case2.The system shows the list of objects y3.The actor selects the object y to delete4.The system deletes the object y

And the second option:

Use case Delete Object

Pre-conditions: AuthenticationPost-Condition: The object is deletedMain scenario:1.The actor starts the use case2.The system asks to the actor if he want to delete object x or object y3.The actor makes his choice4.The system shows the list of objects x5.The actor selects the object x to delete6.The system deletes the object x3.a  1. activate the scenario "Object y"Alternative scenario #1 - Object y1.The system shows the list of objects y2.The actor selects the object y to delete3.The system deletes the object y