diff --git a/.travis.yml b/.travis.yml
index f403b54..9b505d6 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,7 +4,7 @@ rust:
   - beta
   - nightly
 before_script:
-  - wget https://github.com/python/cpython/archive/3.5.zip -O cpython.zip
+  - wget https://github.com/python/cpython/archive/3.6.zip -O cpython.zip
   - unzip cpython.zip
   - cd cpython-*
   - ./configure --prefix=$HOME/.local/
diff --git a/README.md b/README.md
index 76ed500..e28f808 100644
--- a/README.md
+++ b/README.md
@@ -23,7 +23,7 @@ A Python virtual machine, written in Rust.
 
 ## Dependencies
 
-* CPython 3.6 (used as a parser and bytecode compiler). Older versions down to 3.4 should work, but their support is not tested.
+* CPython 3.6 (used as a parser and bytecode compiler).
 * [Rust](https://www.rust-lang.org/downloads.html)
 * [Cargo](https://crates.io/install)
 
diff --git a/src/marshal/mod.rs b/src/marshal/mod.rs
index 11cd6ae..24155a8 100644
--- a/src/marshal/mod.rs
+++ b/src/marshal/mod.rs
@@ -18,6 +18,6 @@ pub fn check_magic(buf: &[u8]) -> bool {
         false
     }
     else {
-        3310 <= version /* ≥ 3.4rc2 */ && version < 3390 /* < 3.7 */
+        3379 <= version /* ≥ 3.6rc1 */ && version < 3390 /* < 3.7 */
     }
 }
diff --git a/src/primitives/mod.rs b/src/primitives/mod.rs
index 538db21..50da2c9 100644
--- a/src/primitives/mod.rs
+++ b/src/primitives/mod.rs
@@ -89,7 +89,9 @@ fn build_class<EP: EnvProxy>(state: &mut State<EP>, call_stack: &mut Vec<Frame>,
     let mut instructions: Vec<Instruction> = InstructionDecoder::new(code.code.iter()).collect();
 
     // Hack to made the class' code return the class instead of None
-    assert_eq!(instructions.pop(), Some(Instruction::ReturnValue));
+    let mut last_instruction;
+    while {last_instruction = instructions.pop(); last_instruction == Some(Instruction::Nop)} {};
+    assert_eq!(last_instruction, Some(Instruction::ReturnValue));
     instructions.pop(); // LoadConst None
     instructions.push(Instruction::PushImmediate(cls_ref.clone()));
     instructions.push(Instruction::ReturnValue);
diff --git a/src/processor/instructions.rs b/src/processor/instructions.rs
index 218e9a2..4d50da3 100644
--- a/src/processor/instructions.rs
+++ b/src/processor/instructions.rs
@@ -18,7 +18,7 @@ pub enum CmpOperator {
 }
 
 impl CmpOperator {
-    pub fn from_bytecode(n: u32) -> Self {
+    pub fn from_bytecode(n: usize) -> Self {
         match n {
             0 => CmpOperator::Lt,
             1 => CmpOperator::Leq,
@@ -69,9 +69,10 @@ pub enum Instruction {
     LoadFast(usize),
     StoreFast(usize),
     LoadGlobal(usize),
-    CallFunction(usize, usize), // nb_args, nb_kwargs
-    RaiseVarargs(u16),
-    MakeFunction(usize, usize, usize), // nb_default_args, nb_default_kwargs, nb_annot
+    CallFunction(usize, bool), // nb_args + nb_kwargs, has_kwargs
+    RaiseVarargs(usize),
+    MakeFunction { has_defaults: bool, has_kwdefaults: bool, has_annotations: bool, has_closure: bool },
+    BuildConstKeyMap(usize),
 }
 
 #[derive(Debug)]
@@ -123,55 +124,65 @@ impl<'a, I> Iterator for InstructionDecoder<I> where I: Iterator<Item=&'a u8> {
             self.pending_nops -= 1;
             return Some(Instruction::Nop)
         };
-        self.bytestream.next().map(|opcode| {
-            match *opcode {
-                1 => Instruction::PopTop,
-                4 => Instruction::DupTop,
-                25 => Instruction::BinarySubscr,
-                68 => Instruction::GetIter,
-                71 => Instruction::LoadBuildClass,
-                83 => Instruction::ReturnValue,
-                87 => Instruction::PopBlock,
-                88 => Instruction::EndFinally,
-                89 => Instruction::PopExcept,
-                90 => Instruction::StoreName(self.read_argument() as usize),
-                93 => Instruction::ForIter(self.read_argument() as usize),
-                95 => Instruction::StoreAttr(self.read_argument() as usize),
-                97 => Instruction::StoreGlobal(self.read_argument() as usize),
-                100 => Instruction::LoadConst(self.read_argument() as usize),
-                101 => Instruction::LoadName(self.read_argument() as usize),
-                102 => Instruction::BuildTuple(self.read_argument() as usize),
-                106 => Instruction::LoadAttr(self.read_argument() as usize),
-                107 => Instruction::CompareOp(CmpOperator::from_bytecode(self.read_argument())),
-                110 => Instruction::JumpForward(self.read_argument() as usize + 2), // +2, because JumpForward takes 3 bytes, and the relative address is computed from the next instruction.
-                113 => Instruction::JumpAbsolute(self.read_argument() as usize),
-                114 => Instruction::PopJumpIfFalse(self.read_argument() as usize),
-                116 => Instruction::LoadGlobal(self.read_argument() as usize),
-                120 => Instruction::SetupLoop(self.read_argument() as usize + 2),
-                121 => Instruction::SetupExcept(self.read_argument() as usize + 2),
-                124 => Instruction::LoadFast(self.read_argument() as usize),
-                125 => Instruction::StoreFast(self.read_argument() as usize),
-                130 => Instruction::RaiseVarargs(self.read_argument() as u16),
-                131 => Instruction::CallFunction(self.read_byte() as usize, self.read_byte() as usize),
-                132 => {
-                    let arg = self.read_argument();
-                    let nb_pos = arg & 0xFF;
-                    let nb_kw = (arg >> 8) & 0xFF;
-                    //let nb_annot = (arg >> 16) & 0x7FF; // TODO
-                    let nb_annot = 0;
-                    Instruction::MakeFunction(nb_pos as usize, nb_kw as usize, nb_annot as usize)
-                },
-                144 => { self.arg_prefix = Some(self.read_argument()); Instruction::Nop },
-                _ => panic!(format!("Opcode not supported: {}", opcode)),
+        let mut opcode = 144;
+        let mut oparg: usize = 0;
+        while opcode == 144 {
+            match self.bytestream.next() {
+                Some(op) => { opcode = *op },
+                None => return None,
             }
-        })
+            oparg = (oparg << 8) | (*self.bytestream.next().unwrap() as usize);
+            self.pending_nops += 1;
+        }
+        self.pending_nops -= 1;
+        let inst = match opcode {
+            1 => Instruction::PopTop,
+            4 => Instruction::DupTop,
+            25 => Instruction::BinarySubscr,
+            68 => Instruction::GetIter,
+            71 => Instruction::LoadBuildClass,
+            83 => Instruction::ReturnValue,
+            87 => Instruction::PopBlock,
+            88 => Instruction::EndFinally,
+            89 => Instruction::PopExcept,
+            90 => Instruction::StoreName(oparg),
+            93 => Instruction::ForIter(oparg),
+            95 => Instruction::StoreAttr(oparg),
+            97 => Instruction::StoreGlobal(oparg),
+            100 => Instruction::LoadConst(oparg),
+            101 => Instruction::LoadName(oparg),
+            102 => Instruction::BuildTuple(oparg),
+            106 => Instruction::LoadAttr(oparg),
+            107 => Instruction::CompareOp(CmpOperator::from_bytecode(oparg)),
+            110 => Instruction::JumpForward(oparg),
+            113 => Instruction::JumpAbsolute(oparg),
+            114 => Instruction::PopJumpIfFalse(oparg),
+            116 => Instruction::LoadGlobal(oparg),
+            120 => Instruction::SetupLoop(oparg + 1),
+            121 => Instruction::SetupExcept(oparg + 1),
+            124 => Instruction::LoadFast(oparg),
+            125 => Instruction::StoreFast(oparg),
+            130 => Instruction::RaiseVarargs(oparg),
+            131 => Instruction::CallFunction(oparg, false),
+            132 => Instruction::MakeFunction {
+                has_defaults: oparg & 0x01 != 0,
+                has_kwdefaults: oparg & 0x02 != 0,
+                has_annotations: oparg & 0x04 != 0,
+                has_closure: oparg & 0x08 != 0,
+            },
+            141 => Instruction::CallFunction(oparg, true),
+            156 => Instruction::BuildConstKeyMap(oparg),
+            144 => panic!("The impossible happened."),
+            _ => panic!(format!("Opcode not supported: {:?}", (opcode, oparg))),
+        };
+        Some(inst)
     }
 }
 
 #[test]
 fn test_load_read() {
-    let bytes: Vec<u8> = vec![124, 1, 0, 83];
+    let bytes: Vec<u8> = vec![124, 1, 83, 0];
     let reader = InstructionDecoder::new(bytes.iter());
     let instructions: Vec<Instruction> = reader.collect();
-    assert_eq!(vec![Instruction::LoadFast(1), Instruction::Nop, Instruction::Nop, Instruction::ReturnValue], instructions);
+    assert_eq!(vec![Instruction::LoadFast(1), Instruction::ReturnValue], instructions);
 }
diff --git a/src/processor/mod.rs b/src/processor/mod.rs
index d419599..0cfa4fa 100644
--- a/src/processor/mod.rs
+++ b/src/processor/mod.rs
@@ -15,6 +15,8 @@ use super::state::{State, PyResult, unwind, raise, return_value};
 use super::sandbox::EnvProxy;
 use super::primitives;
 
+const WORD_SIZE: usize = 2;
+
 #[derive(Debug)]
 pub enum ProcessorError {
     CircularReference,
@@ -233,11 +235,12 @@ fn run_code<EP: EnvProxy>(state: &mut State<EP>, call_stack: &mut Vec<Frame>) ->
             let instruction = py_unwrap!(state, frame.instructions.get(frame.program_counter), ProcessorError::InvalidProgramCounter);
             // Useful for debugging:
             /*
-            println!("");
+            println!("======");
             for r in frame.var_stack.iter() {
                 println!("{}", r.repr(&state.store));
             }
-            println!("{} {:?}", frame.program_counter, instruction);
+            println!("{} {:?}", frame.program_counter*WORD_SIZE, instruction);
+            println!("======");
             */
             frame.program_counter += 1;
             instruction.clone()
@@ -362,7 +365,7 @@ fn run_code<EP: EnvProxy>(state: &mut State<EP>, call_stack: &mut Vec<Frame>) ->
             Instruction::ForIter(i) => {
                 let iterator = {
                     let frame = call_stack.last_mut().unwrap();
-                    frame.block_stack.push(Block::ExceptPopGoto(state.primitive_objects.stopiteration.clone(), 1, frame.program_counter+i));
+                    frame.block_stack.push(Block::ExceptPopGoto(state.primitive_objects.stopiteration.clone(), 1, frame.program_counter+i/WORD_SIZE));
                     let iterator = top_stack!(state, frame.var_stack);
                     iterator.clone()
                 };
@@ -436,7 +439,7 @@ fn run_code<EP: EnvProxy>(state: &mut State<EP>, call_stack: &mut Vec<Frame>) ->
             }
             Instruction::SetupExcept(i) => {
                 let frame = call_stack.last_mut().unwrap();
-                frame.block_stack.push(Block::TryExcept(frame.program_counter, frame.program_counter+i))
+                frame.block_stack.push(Block::TryExcept(frame.program_counter, frame.program_counter+i/WORD_SIZE))
             }
             Instruction::CompareOp(CmpOperator::Eq) => {
                 let frame = call_stack.last_mut().unwrap();
@@ -465,11 +468,11 @@ fn run_code<EP: EnvProxy>(state: &mut State<EP>, call_stack: &mut Vec<Frame>) ->
             }
             Instruction::JumpAbsolute(target) => {
                 let frame = call_stack.last_mut().unwrap();
-                frame.program_counter = target
+                frame.program_counter = target / WORD_SIZE
             }
             Instruction::JumpForward(delta) => {
                 let frame = call_stack.last_mut().unwrap();
-                frame.program_counter += delta
+                frame.program_counter += delta / WORD_SIZE
             }
             Instruction::LoadFast(i) => {
                 let frame = call_stack.last_mut().unwrap();
@@ -487,7 +490,7 @@ fn run_code<EP: EnvProxy>(state: &mut State<EP>, call_stack: &mut Vec<Frame>) ->
                 let obj = state.store.deref(&pop_stack!(state, frame.var_stack));
                 match obj.content {
                     ObjectContent::True => (),
-                    ObjectContent::False => frame.program_counter = target,
+                    ObjectContent::False => frame.program_counter = target / WORD_SIZE,
                     _ => unimplemented!(),
                 }
             }
@@ -509,21 +512,32 @@ fn run_code<EP: EnvProxy>(state: &mut State<EP>, call_stack: &mut Vec<Frame>) ->
                 panic!("Bad RaiseVarargs argument") // TODO: Raise an exception instead
             }
 
-            Instruction::CallFunction(nb_args, nb_kwargs) => {
+            Instruction::CallFunction(nb_args, has_kwargs) => {
                 // See “Call constructs” at:
                 // http://security.coverity.com/blog/2014/Nov/understanding-python-bytecode.html
-                let kwargs;
+                let kwargs: Vec<(ObjectRef, ObjectRef)>;
                 let args;
                 let func;
                 {
                     let frame = call_stack.last_mut().unwrap();
-                    kwargs = py_unwrap!(state, frame.var_stack.pop_n_pairs(nb_kwargs), ProcessorError::StackTooSmall);
-                    args = py_unwrap!(state, frame.var_stack.pop_many(nb_args), ProcessorError::StackTooSmall);
+                    if has_kwargs {
+                        let ref obj = state.store.deref(&pop_stack!(state, frame.var_stack)).content;
+                        let names: Vec<ObjectRef> = match obj {
+                            &ObjectContent::Tuple(ref v) => v.into_iter().cloned().collect(),
+                            _ => panic!("Bad CallFunctionKw argument"),
+                        };
+                        let values: Vec<ObjectRef> = frame.var_stack.pop_many(names.len()).unwrap();
+                        kwargs = names.into_iter().zip(values).collect();
+                    }
+                    else {
+                        kwargs = Vec::new();
+                    }
+                    args = py_unwrap!(state, frame.var_stack.pop_many(nb_args - kwargs.len()), ProcessorError::StackTooSmall);
                     func = pop_stack!(state, frame.var_stack);
                 }
                 call_function(state, call_stack, &func, args, kwargs)
             },
-            Instruction::MakeFunction(0, nb_default_kwargs, 0) => {
+            Instruction::MakeFunction { has_defaults: false, has_kwdefaults, has_annotations: false, has_closure: false } => {
                 // TODO: consume default arguments and annotations
                 let obj = {
                     let frame = call_stack.last_mut().unwrap();
@@ -540,18 +554,35 @@ fn run_code<EP: EnvProxy>(state: &mut State<EP>, call_stack: &mut Vec<Frame>) ->
                 };
                 let frame = call_stack.last_mut().unwrap();
                 let code = pop_stack!(state, frame.var_stack);
-                let raw_kwdefaults = py_unwrap!(state, frame.var_stack.pop_n_pairs(nb_default_kwargs), ProcessorError::StackTooSmall);
                 let mut kwdefaults: HashMap<String, ObjectRef> = HashMap::new();
-                kwdefaults.reserve(nb_default_kwargs);
-                for (key, value) in raw_kwdefaults {
-                    match state.store.deref(&key).content {
-                        ObjectContent::String(ref s) => { kwdefaults.insert(s.clone(), value); },
-                        _ => panic!("Defaults' keys must be strings."),
+                if has_kwdefaults {
+                    let obj = state.store.deref(&pop_stack!(state, frame.var_stack)).content.clone(); // TODO: clone only if necessary
+                    let raw_kwdefaults = match obj {
+                        ObjectContent::Dict(ref d) => d,
+                        _ => panic!("bad type for default kwd"),
+                    };
+                    kwdefaults.reserve(raw_kwdefaults.len());
+                    for &(ref key, ref value) in raw_kwdefaults {
+                        match state.store.deref(&key).content {
+                            ObjectContent::String(ref s) => { kwdefaults.insert(s.clone(), value.clone()); },
+                            _ => panic!("Defaults' keys must be strings."),
+                        }
                     }
                 }
                 let func = state.primitive_objects.new_function(func_name, frame.object.module(&state.store), code, kwdefaults);
                 frame.var_stack.push(state.store.allocate(func))
             },
+            Instruction::BuildConstKeyMap(size) => {
+                let frame = call_stack.last_mut().unwrap();
+                let obj = state.store.deref(&pop_stack!(state, frame.var_stack)).content.clone(); // TODO: clone only if necessary
+                let keys: Vec<ObjectRef> = match obj {
+                    ObjectContent::Tuple(ref v) => v.clone(),
+                    _ => panic!("bad BuildConstKeyMap keys argument."),
+                };
+                let values: Vec<ObjectRef> = frame.var_stack.peek(size).unwrap().iter().map(|r| (*r).clone()).collect();
+                let dict = state.primitive_objects.new_dict(keys.into_iter().zip(values).collect());
+                frame.var_stack.push(state.store.allocate(dict))
+            }
             _ => panic!(format!("todo: instruction {:?}", instruction)),
         }
     };
diff --git a/src/varstack.rs b/src/varstack.rs
index 7bdff47..0e73843 100644
--- a/src/varstack.rs
+++ b/src/varstack.rs
@@ -9,6 +9,7 @@ pub trait VarStack : Debug {
     fn push(&mut self, value: Self::Item);
     fn pop_all_and_get_n_last(&mut self, nb: usize) -> Option<Vec<Self::Item>>;
     fn pop_n_pairs(&mut self, nb: usize) -> Option<Vec<(Self::Item, Self::Item)>>;
+    fn peek(&self, nb: usize) -> Option<Vec<&Self::Item>>;
 }
 
 #[derive(Debug)]
@@ -75,4 +76,13 @@ impl<Item: Clone> VarStack for VectorVarStack<Item> where Item: Debug {
             pairs
         })
     }
+    fn peek(&self, nb: usize) -> Option<Vec<&Self::Item>> {
+        if nb > self.vector.len() {
+            None
+        }
+        else {
+            let length = self.vector.len();
+            Some(self.vector[(length-nb)..length].iter().collect())
+        }
+    }
 }
diff --git a/tests/test_basic.rs b/tests/test_basic.rs
index 9150ad7..951dc51 100644
--- a/tests/test_basic.rs
+++ b/tests/test_basic.rs
@@ -6,14 +6,14 @@ use pythonvm::{MockEnvProxy, PyResult, run_file};
 
 #[test]
 fn test_hello_world() {
-    let mut reader: &[u8] = b"\xee\x0c\r\n\xb0\x92\x0fW\x15\x00\x00\x00\xe3\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00@\x00\x00\x00s\x0e\x00\x00\x00e\x00\x00d\x00\x00\x83\x01\x00\x01d\x01\x00S)\x02z\x0bHello worldN)\x01\xda\x05print\xa9\x00r\x02\x00\x00\x00r\x02\x00\x00\x00\xfa\x16examples/helloworld.py\xda\x08<module>\x01\x00\x00\x00s\x00\x00\x00\x00";
+    let mut reader: &[u8] = b"3\r\r\n\xe1\xc8\xf4Y\x15\x00\x00\x00\xe3\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x02\x00\x00\x00@\x00\x00\x00s\x0c\x00\x00\x00e\x00d\x00\x83\x01\x01\x00d\x01S\x00)\x02z\x0bhello worldN)\x01\xda\x05print\xa9\x00r\x02\x00\x00\x00r\x02\x00\x00\x00\xfa\x16examples/helloworld.py\xda\x08<module>\x01\x00\x00\x00s\x00\x00\x00\x00";
     let mut path = PathBuf::new();
     path.push(env::current_dir().unwrap());
     path.push("pythonlib/");
     let envproxy = MockEnvProxy::new(path);
     let (processor, result) = run_file(&mut reader, envproxy).unwrap();
     if let PyResult::Return(_) = result {
-        assert_eq!(*processor.envproxy.stdout_content.lock().unwrap(), b"Hello world\n");
+        assert_eq!(*processor.envproxy.stdout_content.lock().unwrap(), b"hello world\n");
     }
     else {
         panic!(format!("Exited with: {:?}", result))

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