In mid-December, 1972, Lyndon Baines Johnson attended a civil rights conference at the newly built LBJ Library in Austin, Texas. A second heart attack had taken its toll on the former president, and, as he approached the podium to give what would be his last public address, his feet moved slowly. His voice was low as he stated that the record of the work for racial equality held within the library "holds the most of myself within it and holds for me the most intimate meanings".

Those words mark Johnson as potentially a great man. Yet he was, as the title of this book suggests, a "flawed giant".

By the spring of 1968, his administration was in such disarray that he decided not to run for a second term, and, by this time, liberals and conservatives alike despised him. Since the 1960s, historians have delivered more harsh judgements on LBJ. But Robert Dallek, a historian at Boston University, has now set himself the task of understanding the man and his reputation, and he delivers an appraisal of Johnson that sets forth the president's achievements, as well as his flaws.

Not that anyone can read Dallek's book and remain ignorant of the flaws that brought down the president. Dallek goes so far as to say that Johnson "came frighteningly close to clinical paranoia". His persecution complex made him oversensitive to press criticism, especially concerning the Vietnam conflict, and this closed his mind to reasoned debate that might, conceivably, have resulted in a wiser course.

On one occasion, some reporters asked Johnson in an off-the-record gathering to explain America's participation in Vietnam. There was no satisfactory answer to that question in LBJ's brain, so he unzipped, revealed his not-so private member, and stated: "This is why!" Like other presidents before and since, Johnson found that his libidinous behaviour could be a cause of political weakness.

In keeping with the priapic tendencies of the Kennedy White House, he disported himself in the vice-presidential office with a Hispanic secretary known as "the chili queen". As was the custom in those days, reporters did not discuss publicly the happenings in Johnson's "nooky room". But Dallek speculates that LBJ knew FBI director J. Edgar Hoover would be keeping tabs on his philandering. This gave Hoover "power over Johnson that LBJ understandably feared". This was no light matter, given Hoover's reactionary views and Johnson's agenda of social reform.

Dallek balances all this with a fine narrative of Johnson's presidency and a summation of his achievements in office. Much of the ground covered is familiar, for example LBJ's difficult times with Kennedy, his triumphs against Barry Goldwater and in the call for a Great Society, and the traumas of his disillusionment with the war and fall from grace.

In places, as in his account of the Vietnam conflict, Dallek relies rather heavily on the research of others. However, there is ample compensation in some of the fresh perspectives he offers. For example, he shows that LBJ knew that the Nixon team was using dirty tricks to knife Hubert Humphrey's 1968 presidential campaign, but chose not to expose them because he was ambivalent towards his vice-president's attempt to win the White House. But later, when the Nixon White House was threatening to crush the Watergate investigation, Johnson forced a climb-down by threatening to reveal all about that sordid campaign in 1968.

Dallek sees "a striking analogy" between the accomplishments of Johnson and those of the New Deal. LBJ irrevocably changed the American mindset. He helped to end racial segregation, to establish a kind of national health service, generally to broaden access to education, and to protect the environment. He promoted public broadcasting, greater access to legal services, and national endowments for the arts and humanities.

Dallek even has a constructive explanation of LBJ's sometimes eccentric behaviour - it was designed to confuse his listeners, with the object of lowering their defences and winning them over to his side. Not all these points are convincing. For example, some of LBJ's eccentricity seems less likely to be artifice than the product of confusion in his own mind. But in his well-researched and clearly written book, Dallek has undoubtedly succeeded in introducing a measure of balance to the literature on Johnson.

Flawed Giant will be an automatic purchase for academic libraries and for scholars specialising in 1960s America. Because it is such a fine antidote to the plethora of popular nonsense written about the Kennedy-Johnson era, it also deserves to be given shelf space in every British public library.

Rhodri Jeffreys-Jones is professor of American history, University of Edinburgh.