diff --git a/Tests/images/hopper_I.png b/Tests/images/hopper_I.png
new file mode 100644
index 000000000..314ab09c7
Binary files /dev/null and b/Tests/images/hopper_I.png differ
diff --git a/Tests/test_file_png.py b/Tests/test_file_png.py
index 6a061fe6a..23fa160e7 100644
--- a/Tests/test_file_png.py
+++ b/Tests/test_file_png.py
@@ -295,7 +295,7 @@ class TestFilePng(PillowTestCase):
         for mode, num_transparent in {
             "1": 1994,
             "L": 559,
-            "I": 559,
+            "I": 4096,
         }.items():
             in_file = "Tests/images/"+mode.lower()+"_trns.png"
             im = Image.open(in_file)
diff --git a/Tests/test_image_convert.py b/Tests/test_image_convert.py
index 970dc8ce1..36f2c9d64 100644
--- a/Tests/test_image_convert.py
+++ b/Tests/test_image_convert.py
@@ -38,6 +38,8 @@ class TestImageConvert(PillowTestCase):
 
     def _test_float_conversion(self, im):
         orig = im.getpixel((5, 5))
+        if im.mode[0] == 'I':
+            orig //= 256
         converted = im.convert('F').getpixel((5, 5))
         self.assertEqual(orig, converted)
 
@@ -231,3 +233,11 @@ class TestImageConvert(PillowTestCase):
         # Assert
         # No change
         self.assert_image_equal(converted_im, im)
+
+    def test_i_to_l(self):
+        im = Image.open("Tests/images/hopper_I.png").convert("L")
+        self.assert_image_similar(hopper("L"), im, 0.02)
+
+    def test_i_to_rgb(self):
+        im = Image.open("Tests/images/hopper_I.png").convert("RGB")
+        self.assert_image_similar(hopper("L").convert("RGB"), im, 0.05)
diff --git a/Tests/test_image_getcolors.py b/Tests/test_image_getcolors.py
index aa2a40976..1f4a9b69d 100644
--- a/Tests/test_image_getcolors.py
+++ b/Tests/test_image_getcolors.py
@@ -17,13 +17,13 @@ class TestImageGetColors(PillowTestCase):
 
         self.assertEqual(getcolors("1"), 2)
         self.assertEqual(getcolors("L"), 255)
-        self.assertEqual(getcolors("I"), 255)
         self.assertEqual(getcolors("F"), 255)
         self.assertEqual(getcolors("P"), 90)  # fixed palette
         self.assertIsNone(getcolors("RGB"))
         self.assertIsNone(getcolors("RGBA"))
         self.assertIsNone(getcolors("CMYK"))
         self.assertIsNone(getcolors("YCbCr"))
+        self.assertIsNone(getcolors("I"))
 
         self.assertIsNone(getcolors("L", 128))
         self.assertEqual(getcolors("L", 1024), 255)
diff --git a/Tests/test_image_getdata.py b/Tests/test_image_getdata.py
index fe8f9adcd..56ba39cca 100644
--- a/Tests/test_image_getdata.py
+++ b/Tests/test_image_getdata.py
@@ -21,7 +21,7 @@ class TestImageGetData(PillowTestCase):
 
         self.assertEqual(getdata("1"), (0, 960, 960))
         self.assertEqual(getdata("L"), (16, 960, 960))
-        self.assertEqual(getdata("I"), (16, 960, 960))
+        self.assertEqual(getdata("I"), (4313, 960, 960))
         self.assertEqual(getdata("F"), (16.0, 960, 960))
         self.assertEqual(getdata("RGB"), ((11, 13, 52), 960, 960))
         self.assertEqual(getdata("RGBA"), ((11, 13, 52, 255), 960, 960))
diff --git a/Tests/test_image_getextrema.py b/Tests/test_image_getextrema.py
index 1689744af..985896e20 100644
--- a/Tests/test_image_getextrema.py
+++ b/Tests/test_image_getextrema.py
@@ -11,7 +11,7 @@ class TestImageGetExtrema(PillowTestCase):
 
         self.assertEqual(extrema("1"), (0, 255))
         self.assertEqual(extrema("L"), (0, 255))
-        self.assertEqual(extrema("I"), (0, 255))
+        self.assertEqual(extrema("I"), (150, 65280))
         self.assertEqual(extrema("F"), (0, 255))
         self.assertEqual(extrema("P"), (0, 225))  # fixed palette
         self.assertEqual(
@@ -20,7 +20,7 @@ class TestImageGetExtrema(PillowTestCase):
             extrema("RGBA"), ((0, 255), (0, 255), (0, 255), (255, 255)))
         self.assertEqual(
             extrema("CMYK"), ((0, 255), (0, 255), (0, 255), (0, 0)))
-        self.assertEqual(extrema("I;16"), (0, 255))
+        self.assertEqual(extrema("I;16"), (150, 65280))
 
     def test_true_16(self):
         im = Image.open("Tests/images/16_bit_noise.tif")
diff --git a/Tests/test_image_histogram.py b/Tests/test_image_histogram.py
index 0a023cd69..c70585874 100644
--- a/Tests/test_image_histogram.py
+++ b/Tests/test_image_histogram.py
@@ -11,7 +11,7 @@ class TestImageHistogram(PillowTestCase):
 
         self.assertEqual(histogram("1"), (256, 0, 10994))
         self.assertEqual(histogram("L"), (256, 0, 638))
-        self.assertEqual(histogram("I"), (256, 0, 638))
+        self.assertEqual(histogram("I"), (256, 1, 662))
         self.assertEqual(histogram("F"), (256, 0, 638))
         self.assertEqual(histogram("P"), (256, 0, 1871))
         self.assertEqual(histogram("RGB"), (768, 4, 675))
diff --git a/Tests/test_imagemath.py b/Tests/test_imagemath.py
index 8273b63c1..8acc9420f 100644
--- a/Tests/test_imagemath.py
+++ b/Tests/test_imagemath.py
@@ -31,22 +31,22 @@ class TestImageMath(PillowTestCase):
     def test_sanity(self):
         self.assertEqual(ImageMath.eval("1"), 1)
         self.assertEqual(ImageMath.eval("1+A", A=2), 3)
-        self.assertEqual(pixel(ImageMath.eval("A+B", A=A, B=B)), "I 3")
-        self.assertEqual(pixel(ImageMath.eval("A+B", images)), "I 3")
+        self.assertEqual(pixel(ImageMath.eval("A+B", A=A, B=B)), "I 768")
+        self.assertEqual(pixel(ImageMath.eval("A+B", images)), "I 768")
         self.assertEqual(pixel(ImageMath.eval("float(A)+B", images)), "F 3.0")
         self.assertEqual(pixel(
-            ImageMath.eval("int(float(A)+B)", images)), "I 3")
+            ImageMath.eval("int(float(A)+B)", images)), "I 768")
 
     def test_ops(self):
 
-        self.assertEqual(pixel(ImageMath.eval("-A", images)), "I -1")
+        self.assertEqual(pixel(ImageMath.eval("-A", images)), "I -256")
         self.assertEqual(pixel(ImageMath.eval("+B", images)), "L 2")
 
-        self.assertEqual(pixel(ImageMath.eval("A+B", images)), "I 3")
-        self.assertEqual(pixel(ImageMath.eval("A-B", images)), "I -1")
-        self.assertEqual(pixel(ImageMath.eval("A*B", images)), "I 2")
+        self.assertEqual(pixel(ImageMath.eval("A+B", images)), "I 768")
+        self.assertEqual(pixel(ImageMath.eval("A-B", images)), "I -256")
+        self.assertEqual(pixel(ImageMath.eval("A*B", images)), "I 131072")
         self.assertEqual(pixel(ImageMath.eval("A/B", images)), "I 0")
-        self.assertEqual(pixel(ImageMath.eval("B**2", images)), "I 4")
+        self.assertEqual(pixel(ImageMath.eval("B**2", images)), "I 262144")
         self.assertEqual(pixel(
             ImageMath.eval("B**33", images)), "I 2147483647")
 
@@ -72,61 +72,61 @@ class TestImageMath(PillowTestCase):
             ImageMath.eval("convert(A+B, 'RGB')", images)), "RGB (3, 3, 3)")
 
     def test_compare(self):
-        self.assertEqual(pixel(ImageMath.eval("min(A, B)", images)), "I 1")
-        self.assertEqual(pixel(ImageMath.eval("max(A, B)", images)), "I 2")
-        self.assertEqual(pixel(ImageMath.eval("A == 1", images)), "I 1")
+        self.assertEqual(pixel(ImageMath.eval("min(A, B)", images)), "I 256")
+        self.assertEqual(pixel(ImageMath.eval("max(A, B)", images)), "I 512")
+        self.assertEqual(pixel(ImageMath.eval("A == 256", images)), "I 1")
         self.assertEqual(pixel(ImageMath.eval("A == 2", images)), "I 0")
 
     def test_one_image_larger(self):
-        self.assertEqual(pixel(ImageMath.eval("A+B", A=A2, B=B)), "I 3")
-        self.assertEqual(pixel(ImageMath.eval("A+B", A=A, B=B2)), "I 3")
+        self.assertEqual(pixel(ImageMath.eval("A+B", A=A2, B=B)), "I 768")
+        self.assertEqual(pixel(ImageMath.eval("A+B", A=A, B=B2)), "I 768")
 
     def test_abs(self):
-        self.assertEqual(pixel(ImageMath.eval("abs(A)", A=A)), "I 1")
-        self.assertEqual(pixel(ImageMath.eval("abs(B)", B=B)), "I 2")
+        self.assertEqual(pixel(ImageMath.eval("abs(A)", A=A)), "I 256")
+        self.assertEqual(pixel(ImageMath.eval("abs(B)", B=B)), "I 512")
 
     def test_binary_mod(self):
         self.assertEqual(pixel(ImageMath.eval("A%A", A=A)), "I 0")
         self.assertEqual(pixel(ImageMath.eval("B%B", B=B)), "I 0")
-        self.assertEqual(pixel(ImageMath.eval("A%B", A=A, B=B)), "I 1")
+        self.assertEqual(pixel(ImageMath.eval("A%B", A=A, B=B)), "I 256")
         self.assertEqual(pixel(ImageMath.eval("B%A", A=A, B=B)), "I 0")
         self.assertEqual(pixel(ImageMath.eval("Z%A", A=A, Z=Z)), "I 0")
         self.assertEqual(pixel(ImageMath.eval("Z%B", B=B, Z=Z)), "I 0")
 
     def test_bitwise_invert(self):
         self.assertEqual(pixel(ImageMath.eval("~Z", Z=Z)), "I -1")
-        self.assertEqual(pixel(ImageMath.eval("~A", A=A)), "I -2")
-        self.assertEqual(pixel(ImageMath.eval("~B", B=B)), "I -3")
+        self.assertEqual(pixel(ImageMath.eval("~A", A=A)), "I -257")
+        self.assertEqual(pixel(ImageMath.eval("~B", B=B)), "I -513")
 
     def test_bitwise_and(self):
         self.assertEqual(pixel(ImageMath.eval("Z&Z", A=A, Z=Z)), "I 0")
         self.assertEqual(pixel(ImageMath.eval("Z&A", A=A, Z=Z)), "I 0")
         self.assertEqual(pixel(ImageMath.eval("A&Z", A=A, Z=Z)), "I 0")
-        self.assertEqual(pixel(ImageMath.eval("A&A", A=A, Z=Z)), "I 1")
+        self.assertEqual(pixel(ImageMath.eval("A&A", A=A, Z=Z)), "I 256")
 
     def test_bitwise_or(self):
         self.assertEqual(pixel(ImageMath.eval("Z|Z", A=A, Z=Z)), "I 0")
-        self.assertEqual(pixel(ImageMath.eval("Z|A", A=A, Z=Z)), "I 1")
-        self.assertEqual(pixel(ImageMath.eval("A|Z", A=A, Z=Z)), "I 1")
-        self.assertEqual(pixel(ImageMath.eval("A|A", A=A, Z=Z)), "I 1")
+        self.assertEqual(pixel(ImageMath.eval("Z|A", A=A, Z=Z)), "I 256")
+        self.assertEqual(pixel(ImageMath.eval("A|Z", A=A, Z=Z)), "I 256")
+        self.assertEqual(pixel(ImageMath.eval("A|A", A=A, Z=Z)), "I 256")
 
     def test_bitwise_xor(self):
         self.assertEqual(pixel(ImageMath.eval("Z^Z", A=A, Z=Z)), "I 0")
-        self.assertEqual(pixel(ImageMath.eval("Z^A", A=A, Z=Z)), "I 1")
-        self.assertEqual(pixel(ImageMath.eval("A^Z", A=A, Z=Z)), "I 1")
+        self.assertEqual(pixel(ImageMath.eval("Z^A", A=A, Z=Z)), "I 256")
+        self.assertEqual(pixel(ImageMath.eval("A^Z", A=A, Z=Z)), "I 256")
         self.assertEqual(pixel(ImageMath.eval("A^A", A=A, Z=Z)), "I 0")
 
     def test_bitwise_leftshift(self):
         self.assertEqual(pixel(ImageMath.eval("Z<<0", Z=Z)), "I 0")
         self.assertEqual(pixel(ImageMath.eval("Z<<1", Z=Z)), "I 0")
-        self.assertEqual(pixel(ImageMath.eval("A<<0", A=A)), "I 1")
-        self.assertEqual(pixel(ImageMath.eval("A<<1", A=A)), "I 2")
+        self.assertEqual(pixel(ImageMath.eval("A<<0", A=A)), "I 256")
+        self.assertEqual(pixel(ImageMath.eval("A<<1", A=A)), "I 512")
 
     def test_bitwise_rightshift(self):
         self.assertEqual(pixel(ImageMath.eval("Z>>0", Z=Z)), "I 0")
         self.assertEqual(pixel(ImageMath.eval("Z>>1", Z=Z)), "I 0")
-        self.assertEqual(pixel(ImageMath.eval("A>>0", A=A)), "I 1")
-        self.assertEqual(pixel(ImageMath.eval("A>>1", A=A)), "I 0")
+        self.assertEqual(pixel(ImageMath.eval("A>>0", A=A)), "I 256")
+        self.assertEqual(pixel(ImageMath.eval("A>>1", A=A)), "I 128")
 
     def test_logical_eq(self):
         self.assertEqual(pixel(ImageMath.eval("A==A", A=A)), "I 1")
diff --git a/Tests/test_mode_i16.py b/Tests/test_mode_i16.py
index 80730a312..00caed1f2 100644
--- a/Tests/test_mode_i16.py
+++ b/Tests/test_mode_i16.py
@@ -17,6 +17,8 @@ class TestModeI16(PillowTestCase):
                 xy = x, y
                 p1 = pix1[xy]
                 p2 = pix2[xy]
+                if im1.mode[0] != "I" and im2.mode[0] == "I":
+                    p2 //= 256
                 self.assertEqual(
                     p1, p2,
                     ("got %r from mode %s at %s, expected %r" %
diff --git a/docs/handbook/concepts.rst b/docs/handbook/concepts.rst
index 055821a15..8e4c0d6da 100644
--- a/docs/handbook/concepts.rst
+++ b/docs/handbook/concepts.rst
@@ -25,9 +25,9 @@ Modes
 -----
 
 The ``mode`` of an image defines the type and depth of a pixel in the image.
-Each pixel uses the full range of the bit depth. So a 1-bit pixel has a range
-of 0-1, an 8-bit pixel has a range of 0-255 and so on. The current release
-supports the following standard modes:
+A 1-bit pixel has a range of 0-1, an 8-bit pixel or a 32-bit floating point
+pixel has a range of 0-255, and a 32-bit signed integer has a range of 0-65535.
+These modes are supported:
 
     * ``1`` (1-bit pixels, black and white, stored with one pixel per byte)
     * ``L`` (8-bit pixels, black and white)
diff --git a/src/libImaging/Convert.c b/src/libImaging/Convert.c
index a6fefca32..e3dd87048 100644
--- a/src/libImaging/Convert.c
+++ b/src/libImaging/Convert.c
@@ -231,7 +231,7 @@ rgb2i(UINT8* out_, const UINT8* in, int xsize)
     int x;
     INT32* out = (INT32*) out_;
     for (x = 0; x < xsize; x++, in += 4)
-        *out++ = L24(in) >> 16;
+        *out++ = L24(in) >> 8;
 }
 
 static void
@@ -575,8 +575,8 @@ l2i(UINT8* out_, const UINT8* in, int xsize)
 {
     int x;
     INT32* out = (INT32*) out_;
-    for (x = 0; x < xsize; x++)
-        *out++ = (INT32) *in++;
+    for (x = 0; x < xsize; x++, in++)
+        *out++ = (INT32) (*in << 8);
 }
 
 static void
@@ -585,12 +585,7 @@ i2l(UINT8* out, const UINT8* in_, int xsize)
     int x;
     INT32* in = (INT32*) in_;
     for (x = 0; x < xsize; x++, in++, out++) {
-        if (*in <= 0)
-            *out = 0;
-        else if (*in >= 255)
-            *out = 255;
-        else
-            *out = (UINT8) *in;
+        *out = (UINT8) (*in >> 8);
     }
 }
 
@@ -601,7 +596,7 @@ i2f(UINT8* out_, const UINT8* in_, int xsize)
     INT32* in = (INT32*) in_;
     FLOAT32* out = (FLOAT32*) out_;
     for (x = 0; x < xsize; x++)
-        *out++ = (FLOAT32) *in++;
+        *out++ = (FLOAT32) (*in++ >> 8);
 }
 
 static void
@@ -610,12 +605,7 @@ i2rgb(UINT8* out, const UINT8* in_, int xsize)
     int x;
     INT32* in = (INT32*) in_;
     for (x = 0; x < xsize; x++, in++, out+=4) {
-        if (*in <= 0)
-            out[0] = out[1] = out[2] = 0;
-        else if (*in >= 255)
-            out[0] = out[1] = out[2] = 255;
-        else
-            out[0] = out[1] = out[2] = (UINT8) *in;
+        out[0] = out[1] = out[2] = (UINT8) (*in >> 8);
         out[3] = 255;
     }
 }
@@ -664,7 +654,7 @@ f2i(UINT8* out_, const UINT8* in_, int xsize)
     FLOAT32* in = (FLOAT32*) in_;
     INT32* out = (INT32*) out_;
     for (x = 0; x < xsize; x++)
-        *out++ = (INT32) *in++;
+        *out++ = (INT32) *in++ << 8;
 }
 
 /* ----------------- */
@@ -722,24 +712,22 @@ ycbcr2la(UINT8* out, const UINT8* in, int xsize)
 static void
 I_I16L(UINT8* out, const UINT8* in_, int xsize)
 {
-    int x, v;
+    int x;
     INT32* in = (INT32*) in_;
     for (x = 0; x < xsize; x++, in++) {
-        v = CLIP16(*in);
-        *out++ = (UINT8) v;
-        *out++ = (UINT8) (v >> 8);
+        *out++ = (UINT8) *in;
+        *out++ = (UINT8) (*in >> 8);
     }
 }
 
 static void
 I_I16B(UINT8* out, const UINT8* in_, int xsize)
 {
-    int x, v;
+    int x;
     INT32* in = (INT32*) in_;
     for (x = 0; x < xsize; x++, in++) {
-        v = CLIP16(*in);
-        *out++ = (UINT8) (v >> 8);
-        *out++ = (UINT8) v;
+        *out++ = (UINT8) (*in >> 8);
+        *out++ = (UINT8) *in;
     }
 }
 
@@ -769,7 +757,7 @@ I16L_F(UINT8* out_, const UINT8* in, int xsize)
     int x;
     FLOAT32* out = (FLOAT32*) out_;
     for (x = 0; x < xsize; x++, in += 2)
-        *out++ = (FLOAT32) (in[0] + ((int) in[1] << 8));
+        *out++ = (FLOAT32) in[1];
 }
 
 
@@ -779,7 +767,7 @@ I16B_F(UINT8* out_, const UINT8* in, int xsize)
     int x;
     FLOAT32* out = (FLOAT32*) out_;
     for (x = 0; x < xsize; x++, in += 2)
-        *out++ = (FLOAT32) (in[1] + ((int) in[0] << 8));
+        *out++ = (FLOAT32) in[0];
 }
 
 static void
@@ -787,8 +775,8 @@ L_I16L(UINT8* out, const UINT8* in, int xsize)
 {
     int x;
     for (x = 0; x < xsize; x++, in++) {
+        *out++ = *in << 8;
         *out++ = *in;
-        *out++ = 0;
     }
 }
 
@@ -797,8 +785,8 @@ L_I16B(UINT8* out, const UINT8* in, int xsize)
 {
     int x;
     for (x = 0; x < xsize; x++, in++) {
-        *out++ = 0;
         *out++ = *in;
+        *out++ = *in << 8;
     }
 }
 
@@ -807,10 +795,7 @@ I16L_L(UINT8* out, const UINT8* in, int xsize)
 {
     int x;
     for (x = 0; x < xsize; x++, in += 2)
-        if (in[1] != 0)
-            *out++ = 255;
-        else
-            *out++ = in[0];
+        *out++ = in[1] + (in[0] << 8);
 }
 
 static void
@@ -818,10 +803,7 @@ I16B_L(UINT8* out, const UINT8* in, int xsize)
 {
     int x;
     for (x = 0; x < xsize; x++, in += 2)
-        if (in[0] != 0)
-            *out++ = 255;
-        else
-            *out++ = in[1];
+        *out++ = in[0] + (in[1] << 8);
 }
 
 static struct {
@@ -1020,7 +1002,7 @@ p2i(UINT8* out_, const UINT8* in, int xsize, const UINT8* palette)
     int x;
     INT32* out = (INT32*) out_;
     for (x = 0; x < xsize; x++)
-        *out++ = L(&palette[in[x]*4]) / 1000;
+        *out++ = (L(&palette[in[x]*4]) / 1000) << 8;
 }
 
 static void
@@ -1029,7 +1011,7 @@ pa2i(UINT8* out_, const UINT8* in, int xsize, const UINT8* palette)
     int x;
     INT32* out = (INT32*) out_;
     for (x = 0; x < xsize; x++, in += 4)
-        *out++ = L(&palette[in[0]*4]) / 1000;
+        *out++ = (L(&palette[in[0]*4]) / 1000) << 8;
 }
 
 static void
diff --git a/src/libImaging/Histo.c b/src/libImaging/Histo.c
index b7c1a9834..b330f88f8 100644
--- a/src/libImaging/Histo.c
+++ b/src/libImaging/Histo.c
@@ -135,11 +135,10 @@ ImagingGetHistogram(Imaging im, Imaging imMask, void* minmax)
                 if (imin >= imax)
                     break;
                 ImagingSectionEnter(&cookie);
-                scale = 255.0F / (imax - imin);
                 for (y = 0; y < im->ysize; y++) {
                     INT32* in = im->image32[y];
                     for (x = 0; x < im->xsize; x++) {
-                        i = (int) (((*in++)-imin)*scale);
+                        i = (int) (((*in++)-imin) * 255.0F / (imax - imin));
                         if (i >= 0 && i < 256)
                             h->histogram[i]++;
                     }