JFrame/BoxLayout weird size behavior

Question

I am trying to set the sizes of my JButtons in a JPanel with BoxLayout correctly, but the behavior is beyond weird. It will take the height from JButton.setPreferredSize, but completely ignore the width. This also only works when all buttons are set to the same height. As soon as one is smaller, it will revert all of them to some random minimum size (which isn't even the same for all buttons)

My code is this:

JFrame frame = new JFrame();
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.setSize(800, 500);

JPanel rightPanel = new JPanel();
JPanel leftPanel = new JPanel();
leftPanel.setLayout(new BoxLayout(leftPanel, BoxLayout.PAGE_AXIS));

JButton bBookmarks = new JButton("Bookmarks");
bBookmarks.setPreferredSize(new Dimension(200, 100));
//more buttons with same size

leftPanel.add(bBookmarks);
//more buttons

JSplitPane mainPanel = new JSplitPane(JSplitPane.HORIZONTAL_SPLIT, leftPanel, rightPanel);
mainPanel.setDividerLocation(200);

frame.add(mainPanel);
frame.setResizable(false);
frame.setVisible(true);

This creates this image.

The middle button is always wider than the rest as well. Using frame.pack() doesn't do anything except resizing the frame because the right panel is empty.

What am I doing wrong?

Edit: Should look like this:

Answer 1

Divide and conquer: break the design into small, easy to layout containers. In this case do not place the buttons directly in the left (BoxLayout) container but in a nested JPanel using GridLayout manager.
This ensures that all buttons have the same size:

    JFrame frame = new JFrame();
    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.setLocationRelativeTo(null);

    //add all buttons to a panel using a GridLayout which shows all components having the same size
    JPanel buttons = new JPanel(new GridLayout(0,1));
    JButton bBookmarks = new JButton("Bookmarks");  buttons.add(bBookmarks);
    JButton bPlotter = new JButton("Plotter");      buttons.add(bPlotter);
    JButton bShips = new JButton("Ships");          buttons.add(bShips);

    //add buttons and text area to a panel using BoxLayout
    JPanel leftPanel = new JPanel();
    leftPanel.setPreferredSize(new Dimension(100,400));
    leftPanel.setLayout(new BoxLayout(leftPanel, BoxLayout.PAGE_AXIS));
    leftPanel.add(buttons);
    leftPanel.add(new TextArea(10,30));

    JPanel rightPanel = new JPanel();
    rightPanel.setPreferredSize(new Dimension(600,400));
    rightPanel.add(new JLabel("right pane"));

    JSplitPane mainPanel = new JSplitPane(JSplitPane.HORIZONTAL_SPLIT,true, leftPanel, rightPanel);

    frame.add(mainPanel);
    frame.pack();
    frame.setVisible(true);

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