Emanuel’s problem has been his attempt to position himself as a corrector rather than an enabler of the Chicago police department’s apparent misbehavior. The release last fall of video showing a white officer shooting black teenager Laquan McDonald 16 times sparked the furor. It intensified when it became widely known that the city’s law department, in the months leading up to Emanuel’s reelection bid, had argued in court against releasing the video. Yesterday a judge stated that an attorney in the law department had withheld and lied about evidence in another police shooting; the lawyer quickly resigned. Emanuel had to state his continued support for the law department’s head. Reacting rather than acting, playing defense rather than offense – that’s a bad corner to be stuck in.

Mayer is in a similar spot, under attack by activist investors led by Starboard Value Fund’s Jeff Smith, who on Wednesday called for Mayer to step down. As Yahoo’s (YHOO) share price has declined over the past year, Smith pressed for spinning off the company’s stakes in Alibaba and Yahoo Japan into a separate entity, and Mayer made plans to do that. Then he reversed course and argued Mayer should leave those stakes right where they are in Yahoo and instead spin off the core businesses into a separate company, which she said she’d do. Now, other activists are pushing for her to forget the spinoff, which could take a year to complete, and just sell those core businesses ASAP because they’re losing value by the day. So how will Mayer respond? The answer is almost beside the point. The more important reality is that no one is talking about her strategy to invigorate Yahoo. Investors, advertisers, and the media are instead focused on which end-game move she’ll try next. Not a strong position from which to lead.

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Müller’s disaster at VW is almost four months old and is becoming a textbook example of poor crisis management. More bad news emerges almost daily. On Monday, the U.S. Justice Department sued VW for installing emissions-cheating devices in cars sold in the U.S., greatly increasing the potential fines the company could be forced to pay. VW stock plunged on the news.

A steady drip of new trouble is what crisis managers try hardest to avoid, but that’s just what all three of these leaders are facing. It’s a vicious circle: The longer it goes on, the harder it becomes for a leader to seize control of the situation and start leading again. My judgment is that Mayer’s situation is closest to irretrievable. Emanuel and Müller could yet pull through, though it’s getting more difficult to see how.