In organic chemistry, an anti-Bredt molecule is a bridged molecule with a double bond at the bridgehead.  Bredts rule is the empirical observation that such molecules can only form in large enough ring systems.  For example, two of the following norbornene isomers violate Bredts rule, and are too unstable to prepare:
The rule is named after Julius Bredt, who first discussed it in 1902 and codified it in 1924.   
Bredts rule results from geometric strain: a double bond at a bridgehead atom necessarily must be trans in at least one ring.  For small rings (fewer than eight atoms), a trans alkene cannot be achieved without substantial ring and angle strain (the p orbitals are improperly aligned for a π bond).  Bredts rule also applies to carbocations and, to a lesser degree, via free radicals, because these intermediates also prefer a planar geometry with 120° angles and sp hybridization.  It generally does not apply to hypervalent heteroatoms, although they are commonly written with a formal double bond.  
There has been an active research program to seek anti-Bredt molecules, with success quantified in S, the non-bridgehead atom count.  The above norbornene system has S = 5, and Fawcett originally postulated that stability required S ≥ 9 in bicyclic systems and S ≥ 11 in tricyclic systems.  For bicyclic systems examples now indicate a limit of S ≥ 7, with several such compounds having been prepared. Bridgehead double bonds can be found in some natural products.  
Bredt's rule can predict the viability of competing elimination reactions in a bridged system. For example, the metal alkyl complexes usually decompose quickly via beta elimination, but Bredt strain prevents tetranorbornyl complexes from doing so.  Bicyclo[5.3.1]undecane-11-one-1-carboxylic acid undergoes decarboxylation on heating to 132 °C, but the similar compound bicyclo[2.2.1]heptan-7-one-1-carboxylic acid remains stable beyond 500 °C, because the decarboxylation proceeds through an anti-Bredt enol.  
Bredt's rule may also prevent a molecule from resonating with certain valence bond isomers.  2-Quinuclidonium does not exhibit the usual reactivity of an amide, because the iminoether tautomer would violate the rule.