diff --git a/src/main/java/ch/dissem/msgpack/types/MPInteger.java b/src/main/java/ch/dissem/msgpack/types/MPInteger.java
index 5125717..3a15a27 100644
--- a/src/main/java/ch/dissem/msgpack/types/MPInteger.java
+++ b/src/main/java/ch/dissem/msgpack/types/MPInteger.java
@@ -52,7 +52,7 @@ public class MPInteger implements MPType<Long> {
             } else if (value <= 0xFFFF) {
                 out.write(0xCD);
                 out.write(ByteBuffer.allocate(2).putShort((short) value).array());
-            } else if (value < 0xFFFFFFFFL) {
+            } else if (value <= 0xFFFFFFFFL) {
                 out.write(0xCE);
                 out.write(ByteBuffer.allocate(4).putInt((int) value).array());
             } else {
@@ -60,7 +60,11 @@ public class MPInteger implements MPType<Long> {
                 out.write(ByteBuffer.allocate(8).putLong(value).array());
             }
         } else {
-            if (value >= Byte.MIN_VALUE) {
+            if (value >= -32) {
+                out.write(new byte[]{
+                        (byte) value
+                });
+            } else if (value >= Byte.MIN_VALUE) {
                 out.write(0xD0);
                 out.write(ByteBuffer.allocate(1).put((byte) value).array());
             } else if (value >= Short.MIN_VALUE) {
@@ -125,8 +129,13 @@ public class MPInteger implements MPType<Long> {
                         return new MPInteger(in.read());
                     case 0xCD:
                         return new MPInteger(in.read() << 8 | in.read());
-                    case 0xCE:
-                        return new MPInteger(in.read() << 24 | in.read() << 16 | in.read() << 8 | in.read());
+                    case 0xCE: {
+                        long value = 0;
+                        for (int i = 0; i < 4; i++) {
+                            value = value << 8 | in.read();
+                        }
+                        return new MPInteger(value);
+                    }
                     case 0xCF: {
                         long value = 0;
                         for (int i = 0; i < 8; i++) {
diff --git a/src/main/java/ch/dissem/msgpack/types/Utils.java b/src/main/java/ch/dissem/msgpack/types/Utils.java
index 62f68f7..7bc32a3 100644
--- a/src/main/java/ch/dissem/msgpack/types/Utils.java
+++ b/src/main/java/ch/dissem/msgpack/types/Utils.java
@@ -101,7 +101,7 @@ public class Utils {
         return new MPFloat(value);
     }
 
-    public static MPInteger mp(int value) {
+    public static MPInteger mp(long value) {
         return new MPInteger(value);
     }
 
diff --git a/src/test/java/ch/dissem/msgpack/ReaderTest.java b/src/test/java/ch/dissem/msgpack/ReaderTest.java
index 1504f88..6066bd0 100644
--- a/src/test/java/ch/dissem/msgpack/ReaderTest.java
+++ b/src/test/java/ch/dissem/msgpack/ReaderTest.java
@@ -100,6 +100,50 @@ public class ReaderTest {
         assertThat(actual.getPrecision(), is(MPFloat.Precision.FLOAT64));
     }
 
+    @Test
+    public void ensureLongsAreEncodedAndDecodedCorrectly() throws Exception {
+        // positive fixnum
+        ensureLongIsEncodedAndDecodedCorrectly(0, 1);
+        ensureLongIsEncodedAndDecodedCorrectly(127, 1);
+        // negative fixnum
+        ensureLongIsEncodedAndDecodedCorrectly(-1, 1);
+        ensureLongIsEncodedAndDecodedCorrectly(-32, 1);
+        // uint 8
+        ensureLongIsEncodedAndDecodedCorrectly(128, 2);
+        ensureLongIsEncodedAndDecodedCorrectly(255, 2);
+        // uint 16
+        ensureLongIsEncodedAndDecodedCorrectly(256, 3);
+        ensureLongIsEncodedAndDecodedCorrectly(65535, 3);
+        // uint 32
+        ensureLongIsEncodedAndDecodedCorrectly(65536, 5);
+        ensureLongIsEncodedAndDecodedCorrectly(4294967295L, 5);
+        // uint 64
+        ensureLongIsEncodedAndDecodedCorrectly(4294967296L, 9);
+        ensureLongIsEncodedAndDecodedCorrectly(Long.MAX_VALUE, 9);
+        // int 8
+        ensureLongIsEncodedAndDecodedCorrectly(-33, 2);
+        ensureLongIsEncodedAndDecodedCorrectly(-128, 2);
+        // int 16
+        ensureLongIsEncodedAndDecodedCorrectly(-129, 3);
+        ensureLongIsEncodedAndDecodedCorrectly(-32768, 3);
+        // int 32
+        ensureLongIsEncodedAndDecodedCorrectly(-32769, 5);
+        ensureLongIsEncodedAndDecodedCorrectly(Integer.MIN_VALUE, 5);
+        // int 64
+        ensureLongIsEncodedAndDecodedCorrectly(-2147483649L, 9);
+        ensureLongIsEncodedAndDecodedCorrectly(Long.MIN_VALUE, 9);
+    }
+
+    private void ensureLongIsEncodedAndDecodedCorrectly(long val, int bytes) throws Exception {
+        MPInteger value = mp(val);
+        ByteArrayOutputStream out = new ByteArrayOutputStream();
+        value.pack(out);
+        MPType read = reader.read(new ByteArrayInputStream(out.toByteArray()));
+        assertThat(out.size(), is(bytes));
+        assertThat(read, instanceOf(MPInteger.class));
+        assertThat((MPInteger) read, is(value));
+    }
+
     @Test
     public void ensureStringsAreEncodedAndDecodedCorrectly() throws Exception {
         ensureStringIsEncodedAndDecodedCorrectly(0);