High is used with these nouns:
ability, abundance, accolade, accuracy, achievement, aim, alert, altar, altitude, ambition, amount, arc, art, aspiration, ball, beam, bid, bill, blood pressure, boot, bracket, bridge, buzz, capacity, caste, casualty, category, ceiling, chance, charge, cheekbone, chimney, cholesterol, church, circle, cliff, cloud, collar, colour, comedy, command, commission, commissioner, concentration, confidence, consumption, content, correlation, cost, count, credibility, culture, cupboard, current, debt, degree, demand, density, desert, diversity, dividend, division, dosage, dose, drama, duty, earnings, effectiveness, efficiency, employment, end, enrolment, esteem, estimate, excitement, expectation, expenditure, expense, explosive, exposure, fare, fashion, fat, favour, fee, fence, fever, figure, finance, forehead, frequency, gate, gear, gloss, grade, ground, growth, heat, hedge, heel, hill, honour, hope, humidity, hurdle, ideal, impact, importance, incidence, income, index, indignation, inflation, intake, integrity, intelligence, intensity, investment, jump, key, kick, latitude, ledge, level, likelihood, load, maintenance, margin, mark, mileage, moral, morale, mortality, motivation, motive, mound, mountain, neck, noon, note, number, occurrence, odds, offer, office, opinion, orbit, output, pass, pay, peak, penetration, percentage, performance, pitch, plateau, platform, point, position, post, potential, prairie, praise, precision, premium, pressure, prestige, price, priest, principle, priority, probability, productivity, proficiency, profile, profit, profitability, proportion, purity, quality, rainfall, rank, rate, rating, ratio, reading, recommendation, regard, register, reliability, relief, rent, reputation, resistance, resolution, respect, return, rev, reward, risk, river, road, room, salary, sale, school, score, season, sensitivity, seriousness, setting, shelf, society, sound, specification, speed, speed limit, spending, spot, squeak, stake, standard, standing, status, stock, stool, street, strength, stress, sum, summer, summit, sun, table, tackle, target, tariff, tax, taxation, tea, technology, temperature, tenor, tension, threshold, tide, tolerance, toll, total, tower, treason, tree, turnout, turnover, uncertainty, unemployment, usage, utility, valley, valuation, value, variability, velocity, visibility, voice, voltage, volume, wage, waist, waistline, wall, wastage, waterfall, whine, whistle, wind, wire, yield

High is used with these adjectives:
overhead

High is used with these verbs:
bounce, climb, fly, leap, rank, soar