Such ordinance shall specify the boundaries of the proposed improvement district and shall describe the lands which it is proposed to assess for said improvement. If any parcel of land within the boundaries of such proposed improvement district has been wholly filled to the proposed grade elevation of the proposed fill, such parcel of land may be excluded from the lists of lands to be assessed, when in the opinion of the city council justice and equity require its exclusion. The boundaries of any improvement district may be altered so as to exclude land therefrom at any time up to the levying of the assessment but such changing of the boundaries shall be by ordinance.