设置EditText的指定高度

Is it an option to explicitly set the height?

If yes, use something like

<EditText
    android:id="@+id/smallEditText"
    android:layout_width="wrap_content"
    android:layout_height="10dip"/>

You can decrease the font size, by using android:textSize in XML. You can also make your control scrollable.

Edit: Just saw your screenshots, what is the layout in which you have put the EditText? It may be setting non-explicit layout rules for your control.