diff --git a/src/ol/proj/chprojection.js b/src/ol/proj/chprojection.js
index 28fccc6614..3302674635 100644
--- a/src/ol/proj/chprojection.js
+++ b/src/ol/proj/chprojection.js
@@ -3,8 +3,10 @@ goog.provide('ol.proj.EPSG2056');
 goog.provide('ol.proj.EPSG21781');
 
 goog.require('goog.asserts');
+goog.require('goog.math');
 goog.require('ol.Projection');
 goog.require('ol.ProjectionUnits');
+goog.require('ol.ellipsoid.BESSEL1841');
 goog.require('ol.proj');
 goog.require('ol.proj.EPSG4326');
 
@@ -27,6 +29,92 @@ ol.proj.CH = function(options) {
 goog.inherits(ol.proj.CH, ol.Projection);
 
 
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.PHI0 = goog.math.toRadians((3600 * 46 + 60 * 57 + 8.66) / 3600);
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.LAMBDA0 = goog.math.toRadians((3600 * 7 + 60 * 26 + 22.5) / 3600);
+
+
+/**
+ * @const
+ * @type {ol.Ellipsoid}
+ */
+ol.proj.CH.ELLIPSOID = ol.ellipsoid.BESSEL1841;
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.COS_PHI0 = Math.cos(ol.proj.CH.PHI0);
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.SIN_PHI0 = Math.sin(ol.proj.CH.PHI0);
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.R = ol.proj.CH.ELLIPSOID.a * Math.sqrt(1 -
+    ol.proj.CH.ELLIPSOID.eSquared) / (1 - ol.proj.CH.ELLIPSOID.eSquared *
+    ol.proj.CH.SIN_PHI0 * ol.proj.CH.SIN_PHI0);
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.ALPHA = Math.sqrt(1 +
+    ol.proj.CH.ELLIPSOID.eSquared * Math.pow(ol.proj.CH.COS_PHI0, 4) /
+    (1 - ol.proj.CH.ELLIPSOID.eSquared));
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.SIN_B0 = ol.proj.CH.SIN_PHI0 / ol.proj.CH.ALPHA;
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.B0 = Math.asin(ol.proj.CH.SIN_B0);
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.COS_B0 = Math.cos(ol.proj.CH.B0);
+// FIXME should we use Math.sqrt(1 - ol.proj.CH.SIN_B0 * ol.proj.CH.SIN_B0) ?
+
+
+/**
+ * @const
+ * @type {number}
+ */
+ol.proj.CH.K = Math.log(Math.tan(Math.PI / 4 + ol.proj.CH.B0 / 2)) -
+    ol.proj.CH.ALPHA * Math.log(Math.tan(Math.PI / 4 + ol.proj.CH.PHI0 / 2)) +
+    ol.proj.CH.ALPHA * ol.proj.CH.ELLIPSOID.e * Math.log(
+        (1 + ol.proj.CH.ELLIPSOID.e * ol.proj.CH.SIN_PHI0) /
+        (1 - ol.proj.CH.ELLIPSOID.e * ol.proj.CH.SIN_PHI0)) / 2;
+
+
 /**
  * Add EPSG:2056 and EPSG:21781 projections, and transformations between them.
  */
@@ -57,7 +145,7 @@ ol.proj.CH.add = function() {
  * @private
  * @return {Array.<number>} Output array of coordinate values.
  */
-ol.proj.CH.fromEPSG4326_ =
+ol.proj.CH.fromEPSG4326Approximate_ =
     function(offsetY, offsetX, input, opt_output, opt_dimension) {
   var n = input.length;
   var dimension = goog.isDef(opt_dimension) ? opt_dimension : 2;
@@ -93,6 +181,57 @@ ol.proj.CH.fromEPSG4326_ =
 };
 
 
+/**
+ * Transformation from EPSG:4326 to EPSG:2056/EPSG:21781.
+ *
+ * @see http://www.swisstopo.admin.ch/internet/swisstopo/en/home/topics/survey/sys/refsys/projections.html
+ *
+ * @param {number} offsetY Y offset.
+ * @param {number} offsetX X offset.
+ * @param {Array.<number>} input Input array of coordinate values.
+ * @param {Array.<number>=} opt_output Output array of coordinate values.
+ * @param {number=} opt_dimension Dimension (default is 2).
+ * @private
+ * @return {Array.<number>} Output array of coordinate values.
+ */
+ol.proj.CH.fromEPSG4326Rigorous_ =
+    function(offsetY, offsetX, input, opt_output, opt_dimension) {
+  var n = input.length;
+  var dimension = goog.isDef(opt_dimension) ? opt_dimension : 2;
+  var output;
+  if (goog.isDef(opt_output)) {
+    output = opt_output;
+  } else {
+    if (dimension > 2) {
+      output = input.slice();
+    } else {
+      output = new Array(n);
+    }
+  }
+  goog.asserts.assert(dimension >= 2);
+  goog.asserts.assert(output.length % dimension === 0);
+  var b, bBar, eSinPhi, i, l, lambda, lBar, phi, s;
+  for (i = 0; i < n; i += dimension) {
+    lambda = goog.math.toRadians(input[i]);
+    phi = goog.math.toRadians(input[i + 1]);
+    eSinPhi = ol.proj.CH.ELLIPSOID.e * Math.sin(phi);
+    s = ol.proj.CH.ALPHA * Math.log(Math.tan(Math.PI / 4 + phi / 2)) -
+        ol.proj.CH.ALPHA * ol.proj.CH.ELLIPSOID.e * Math.log(
+            (1 + eSinPhi) / (1 - eSinPhi)) / 2 + ol.proj.CH.K;
+    b = 2 * (Math.atan(Math.exp(s)) - Math.PI / 4);
+    l = ol.proj.CH.ALPHA * (lambda - ol.proj.CH.LAMBDA0);
+    lBar = Math.atan2(Math.sin(l),
+        ol.proj.CH.SIN_B0 * Math.tan(b) + ol.proj.CH.COS_B0 * Math.cos(l));
+    bBar = Math.asin(ol.proj.CH.COS_B0 * Math.sin(b) -
+        ol.proj.CH.SIN_B0 * Math.cos(b) * Math.cos(l));
+    output[i] = offsetY + ol.proj.CH.R * lBar;
+    output[i + 1] = offsetX + ol.proj.CH.R *
+        Math.log((1 + Math.sin(bBar)) / (1 - Math.sin(bBar))) / 2;
+  }
+  return output;
+};
+
+
 /**
  * Transformation from EPSG:2056/EPSG:21781 to EPSG:4326.
  *
@@ -108,7 +247,7 @@ ol.proj.CH.fromEPSG4326_ =
  * @private
  * @return {Array.<number>} Output array of coordinate values.
  */
-ol.proj.CH.toEPSG4326_ =
+ol.proj.CH.toEPSG4326Approximate_ =
     function(offsetY, offsetX, input, opt_output, opt_dimension) {
   var n = input.length;
   var dimension = goog.isDef(opt_dimension) ? opt_dimension : 2;
@@ -144,6 +283,67 @@ ol.proj.CH.toEPSG4326_ =
 };
 
 
+/**
+ * Transformation from EPSG:2056/EPSG:21781 to EPSG:4326.
+ *
+ * @see http://www.swisstopo.admin.ch/internet/swisstopo/en/home/topics/survey/sys/refsys/projections.html
+ *
+ * @param {number} offsetY Y offset.
+ * @param {number} offsetX X offset.
+ * @param {Array.<number>} input Input array of coordinate values.
+ * @param {Array.<number>=} opt_output Output array of coordinate values.
+ * @param {number=} opt_dimension Dimension (default is 2).
+ * @private
+ * @return {Array.<number>} Output array of coordinate values.
+ */
+ol.proj.CH.toEPSG4326Rigorous_ =
+    function(offsetY, offsetX, input, opt_output, opt_dimension) {
+  var n = input.length;
+  var dimension = goog.isDef(opt_dimension) ? opt_dimension : 2;
+  var output;
+  if (goog.isDef(opt_output)) {
+    output = opt_output;
+  } else {
+    if (dimension > 2) {
+      output = input.slice();
+    } else {
+      output = new Array(n);
+    }
+  }
+  goog.asserts.assert(dimension >= 2);
+  goog.asserts.assert(output.length % dimension === 0);
+  var b, bBar, eSinPhi, i, iterations, l, lambda, lastPhi, lBar, phi, s, x, y;
+  for (i = 0; i < n; i += dimension) {
+    y = input[i] - offsetY;
+    x = input[i + 1] - offsetX;
+    lBar = y / ol.proj.CH.R;
+    bBar = 2 * (Math.atan(Math.exp(x / ol.proj.CH.R)) - Math.PI / 4);
+    b = Math.asin(ol.proj.CH.COS_B0 * Math.sin(bBar) +
+        ol.proj.CH.SIN_B0 * Math.cos(bBar) * Math.cos(lBar));
+    l = Math.atan2(Math.sin(lBar), ol.proj.CH.COS_B0 * Math.cos(lBar) -
+        ol.proj.CH.SIN_B0 * Math.tan(bBar));
+    lambda = ol.proj.CH.LAMBDA0 + l / ol.proj.CH.ALPHA;
+    lastPhi = phi = b;
+    // Empirically, about 18 iterations are required for 1e-7 radian accuracy
+    for (iterations = 20; iterations > 0; --iterations) {
+      s = (Math.log(Math.tan(Math.PI / 4 + b / 2)) -
+          ol.proj.CH.K) / ol.proj.CH.ALPHA +
+          ol.proj.CH.ELLIPSOID.e * Math.log(Math.tan(Math.PI / 4 +
+              Math.asin(ol.proj.CH.ELLIPSOID.e * Math.sin(phi)) / 2));
+      phi = 2 * Math.atan(Math.exp(s)) - Math.PI / 2;
+      if (Math.abs(phi - lastPhi) < 1e-7) {
+        break;
+      }
+      lastPhi = phi;
+    }
+    goog.asserts.assert(iterations !== 0);
+    output[i] = goog.math.toDegrees(lambda);
+    output[i + 1] = goog.math.toDegrees(phi);
+  }
+  return output;
+};
+
+
 /**
  * Transformation between EPSG:2056 and EPSG:21781.
  *
@@ -223,8 +423,8 @@ ol.proj.EPSG2056.add = function() {
   ol.proj.addEquivalentTransforms(
       ol.proj.EPSG4326.PROJECTIONS,
       [epsg2056],
-      goog.partial(ol.proj.CH.fromEPSG4326_, 2600000, 1200000),
-      goog.partial(ol.proj.CH.toEPSG4326_, 2600000, 1200000));
+      goog.partial(ol.proj.CH.fromEPSG4326Rigorous_, 2600000, 1200000),
+      goog.partial(ol.proj.CH.toEPSG4326Rigorous_, 2600000, 1200000));
 };
 
 
@@ -260,6 +460,6 @@ ol.proj.EPSG21781.add = function() {
   ol.proj.addEquivalentTransforms(
       ol.proj.EPSG4326.PROJECTIONS,
       [epsg21781],
-      goog.partial(ol.proj.CH.fromEPSG4326_, 600000, 200000),
-      goog.partial(ol.proj.CH.toEPSG4326_, 600000, 200000));
+      goog.partial(ol.proj.CH.fromEPSG4326Rigorous_, 600000, 200000),
+      goog.partial(ol.proj.CH.toEPSG4326Rigorous_, 600000, 200000));
 };
diff --git a/test/spec/ol/proj/chprojection.test.js b/test/spec/ol/proj/chprojection.test.js
index 23f9ea1a22..a4a814c595 100644
--- a/test/spec/ol/proj/chprojection.test.js
+++ b/test/spec/ol/proj/chprojection.test.js
@@ -9,6 +9,17 @@ describe('ol.proj.CH', function() {
     ol.proj.CH.add();
   });
 
+  it('has the correct constants', function() {
+    expect(ol.proj.CH.ELLIPSOID.eSquared).to.roughlyEqual(
+        0.006674372230614, 1e-13);
+    expect(ol.proj.CH.R).to.roughlyEqual(6378815.90365, 1e-5);
+    expect(ol.proj.CH.ALPHA).to.roughlyEqual(1.00072913843038, 1e-14);
+    expect(ol.proj.CH.B0).to.roughlyEqual(
+        goog.math.toRadians((3600 * 46 + 60 * 54 + 27.83324844) / 3600),
+        1e-13);
+    expect(ol.proj.CH.K).to.roughlyEqual(0.0030667323772751, 1e-13);
+  });
+
   it('can transform from EPSG:2056 to EPSG:21781', function() {
     var output = ol.proj.transform(
         [2660389.515487, 1185731.630396], 'EPSG:2056', 'EPSG:21781');
@@ -41,19 +52,24 @@ describe('ol.proj.EPSG2056', function() {
 
   it('transforms from EPSG:2056 to EPSG:4326', function() {
     var wgs84 = ol.proj.transform(
-        [2660389.515487, 1185731.630396], 'EPSG:2056', 'EPSG:4326');
+        [2679520.05, 1212273.44], 'EPSG:2056', 'EPSG:4326');
     expect(wgs84).to.be.an(Array);
     expect(wgs84).to.have.length(2);
-    expect(wgs84[0]).to.roughlyEqual(8.23, 1e-3);
-    expect(wgs84[1]).to.roughlyEqual(46.82, 1e-3);
+    expect(wgs84[0]).to.roughlyEqual(
+        (3600 * 8 + 60 * 29 + 11.111272) / 3600, 1e-8);
+    expect(wgs84[1]).to.roughlyEqual(
+        (3600 * 47 + 60 * 3 + 28.956592) / 3600, 1e-8);
   });
 
   it('transforms from EPSG:4326 to EPSG:2056', function() {
-    var ch1903 = ol.proj.transform([8.23, 46.82], 'EPSG:4326', 'EPSG:2056');
-    expect(ch1903).to.be.an(Array);
-    expect(ch1903).to.have.length(2);
-    expect(ch1903[0]).to.roughlyEqual(2660389.515487, 1);
-    expect(ch1903[1]).to.roughlyEqual(1185731.630396, 1);
+    var lv95 = ol.proj.transform([
+      (3600 * 8 + 60 * 29 + 11.11127154) / 3600,
+      (3600 * 47 + 60 * 3 + 28.95659233) / 3600
+    ], 'EPSG:4326', 'EPSG:2056');
+    expect(lv95).to.be.an(Array);
+    expect(lv95).to.have.length(2);
+    expect(lv95[0]).to.roughlyEqual(2679520.05, 1e-3);
+    expect(lv95[1]).to.roughlyEqual(1212273.44, 1e-3);
   });
 
 });
@@ -69,7 +85,7 @@ describe('ol.proj.EPSG21781', function() {
     expect(epsg21781).to.be.an(ol.Projection);
   });
 
-  it('does not lose too much accuracy when round-tripping', function() {
+  it('maintains accuracy when round-tripping', function() {
     var extent = epsg21781.getExtent();
     var fromEPSG4326 = ol.proj.getTransform('EPSG:4326', 'EPSG:21781');
     var toEPSG4326 = ol.proj.getTransform('EPSG:21781', 'EPSG:4326');
@@ -79,32 +95,38 @@ describe('ol.proj.EPSG21781', function() {
         roundTripped = fromEPSG4326(toEPSG4326([x, y]));
         expect(roundTripped).to.be.an(Array);
         expect(roundTripped).to.have.length(2);
-        expect(roundTripped[0]).to.roughlyEqual(x, 1e1);
-        expect(roundTripped[1]).to.roughlyEqual(y, 1e1);
+        expect(roundTripped[0]).to.roughlyEqual(x, 1e-3);
+        expect(roundTripped[1]).to.roughlyEqual(y, 1e-3);
       }
     }
   });
 
   it('transforms from EPSG:21781 to EPSG:4326', function() {
     var wgs84 = ol.proj.transform(
-        [660389.515487, 185731.630396], 'EPSG:21781', 'EPSG:4326');
+        [679520.05, 212273.44], 'EPSG:21781', 'EPSG:4326');
     expect(wgs84).to.be.an(Array);
     expect(wgs84).to.have.length(2);
-    expect(wgs84[0]).to.roughlyEqual(8.23, 1e-3);
-    expect(wgs84[1]).to.roughlyEqual(46.82, 1e-3);
+    expect(wgs84[0]).to.roughlyEqual(
+        (3600 * 8 + 60 * 29 + 11.111272) / 3600, 1e-8);
+    expect(wgs84[1]).to.roughlyEqual(
+        (3600 * 47 + 60 * 3 + 28.956592) / 3600, 1e-8);
   });
 
   it('transforms from EPSG:4326 to EPSG:21781', function() {
-    var ch1903 = ol.proj.transform([8.23, 46.82], 'EPSG:4326', 'EPSG:21781');
-    expect(ch1903).to.be.an(Array);
-    expect(ch1903).to.have.length(2);
-    expect(ch1903[0]).to.roughlyEqual(660389.515487, 1);
-    expect(ch1903[1]).to.roughlyEqual(185731.630396, 1);
+    var lv03 = ol.proj.transform([
+      (3600 * 8 + 60 * 29 + 11.11127154) / 3600,
+      (3600 * 47 + 60 * 3 + 28.95659233) / 3600
+    ], 'EPSG:4326', 'EPSG:21781');
+    expect(lv03).to.be.an(Array);
+    expect(lv03).to.have.length(2);
+    expect(lv03[0]).to.roughlyEqual(679520.05, 1e-3);
+    expect(lv03[1]).to.roughlyEqual(212273.44, 1e-3);
   });
 
 });
 
 
+goog.require('goog.math');
 goog.require('ol.Projection');
 goog.require('ol.proj');
 goog.require('ol.proj.CH');