Rolling your own babel-jest

jest.config.js

/*
Up to you how to let Jest consume this config. I ended up stringifying the export and supplying it to a terminal command.
*/

const path = require('path')

module.exports = {
  transform: path.resolve(__dirname, './my-babel-jest.js')
}

my-babel-jest.js

/*
We can recreate what babel-jest does, but skip using .babelrc for any configuration of presets.
*/

const babelJest = require('babel-jest');
const es2015Preset = require('babel-preset-es2015');
const reactPreset = require('babel-preset-react');
const stage2Preset = require('babel-preset-stage-1');
const createBabelJestTransformer = babelJest.createTransformer; // Undocumented feature AFAIK

module.exports = createBabelJestTransformer({
  presets: [ es2015Preset, stage2Preset, reactPreset ]
});

Updated to use transform, rather than deprecated scriptPreprocessor.