With the help from @weeman, I have implemented the following solution. Works both for larger and smaller content, preserves the rounded corners on iOS:
ion-popover-view.fit {
height: auto;
}
ion-popover-view.fit ion-content {
position: relative;
}
.platform-android ion-popover-view.fit {
margin-top: 10px;
}
.platform-ios ion-popover-view.fit {
padding-top: 10px;
padding-bottom: 10px;
}
See the demo: http://codepen.io/vladius/pen/VLEOQo
Note, that I have also disabled the menu scroll for this demo.