Someone asked an excellent question about drilling deeper into the strategy, so I'm going to discuss that tactic, first.
When I talk about drilling deeper, I'm definitely talking about a strategic planning process that involves the top management team, and not external stakeholders or media. When you take planning outside the organization, you are generally looking to communicate why your strategy is a good one rather than how you came up with it. An example of what I mean by "drilling down" could be seen in an airline examining the customer satisfaction impact of all the contact points a passenger may have with them. This might involve some detailed analysis of the operation, combined with insights from market research on things that affect customer satisfaction. While it would look tactical to an outside observer, this kind of "drilling down" can identify places where operational, financial, IT or HR practices (to name a few) can be changed to be better aligned with the overall corporate strategy.
This kind of work is unlikely to be productive with the media, because it is time-consuming and hard for them to package. They will, however, appreciate any surprising bit you might come up with. For example, when Sears acquired K-mart, they saw the real estate involved as the key piece of the value of that deal. This was interesting, because it was a merger of two huge retail brands, not just a real estate transaction. The news media were fascinated by this, without really knowing why that made sense for Sears.
Outside stakeholders may have more appreciation for the actual "drill down" process. The best way to handle this with them (if you have the resources) is to walk them through the key questions. They won't have the data or experience of the management team, but - if you are well-prepared - you can throw those in as trump cards to move the conversation and its conclusions along.
One important point here is that the process of strategic planning is entirely different from the process of communicating the strategic plan. Both are important, but it's possible to do either poorly if you mix them together without considering how you will affect the quality of the strategy or the perception of the resulting plan.