diff --git a/eth2/state_processing/src/common/exit_validator.rs b/eth2/state_processing/src/common/exit_validator.rs
deleted file mode 100644
index 7a817b126..000000000
--- a/eth2/state_processing/src/common/exit_validator.rs
+++ /dev/null
@@ -1,22 +0,0 @@
-use types::{BeaconStateError as Error, *};
-
-/// Exit the validator of the given `index`.
-///
-/// Spec v0.5.1
-pub fn exit_validator<T: EthSpec>(
-    state: &mut BeaconState<T>,
-    validator_index: usize,
-    spec: &ChainSpec,
-) -> Result<(), Error> {
-    if validator_index >= state.validator_registry.len() {
-        return Err(Error::UnknownValidator);
-    }
-
-    let delayed_epoch = state.get_delayed_activation_exit_epoch(state.current_epoch(), spec);
-
-    if state.validator_registry[validator_index].exit_epoch > delayed_epoch {
-        state.validator_registry[validator_index].exit_epoch = delayed_epoch;
-    }
-
-    Ok(())
-}
diff --git a/eth2/state_processing/src/per_epoch_processing.rs b/eth2/state_processing/src/per_epoch_processing.rs
index 5253cd95c..5e37877e4 100644
--- a/eth2/state_processing/src/per_epoch_processing.rs
+++ b/eth2/state_processing/src/per_epoch_processing.rs
@@ -161,7 +161,8 @@ pub fn process_crosslinks<T: EthSpec>(
     for relative_epoch in vec![RelativeEpoch::Previous, RelativeEpoch::Current] {
         let epoch = relative_epoch.into_epoch(state.current_epoch());
         for offset in 0..state.get_epoch_committee_count(relative_epoch)? {
-            let shard = (state.get_epoch_start_shard(relative_epoch)? + offset) % spec.shard_count;
+            let shard =
+                (state.get_epoch_start_shard(relative_epoch)? + offset) % T::ShardCount::to_u64();
             let crosslink_committee =
                 state.get_crosslink_committee_for_shard(shard, relative_epoch)?;
 
diff --git a/eth2/state_processing/src/per_epoch_processing/validator_statuses.rs b/eth2/state_processing/src/per_epoch_processing/validator_statuses.rs
index a4062b988..a2ce292eb 100644
--- a/eth2/state_processing/src/per_epoch_processing/validator_statuses.rs
+++ b/eth2/state_processing/src/per_epoch_processing/validator_statuses.rs
@@ -248,7 +248,7 @@ impl ValidatorStatuses {
                     status.is_previous_epoch_target_attester = true;
                 }
 
-                if has_common_beacon_block_root(a, state, spec)? {
+                if has_common_beacon_block_root(a, state)? {
                     status.is_previous_epoch_head_attester = true;
                 }
             }
@@ -298,8 +298,7 @@ impl ValidatorStatuses {
     ) -> Result<(), BeaconStateError> {
         // Loop through each slot in the previous epoch.
         for slot in state.previous_epoch().slot_iter(spec.slots_per_epoch) {
-            let crosslink_committees_at_slot =
-                state.get_crosslink_committees_at_slot(slot, spec)?;
+            let crosslink_committees_at_slot = state.get_crosslink_committees_at_slot(slot)?;
 
             // Loop through each committee in the slot.
             for c in crosslink_committees_at_slot {
@@ -352,7 +351,6 @@ fn target_matches_epoch_start_block<T: EthSpec>(
 fn has_common_beacon_block_root<T: EthSpec>(
     a: &PendingAttestation,
     state: &BeaconState<T>,
-    spec: &ChainSpec,
 ) -> Result<bool, BeaconStateError> {
     let attestation_slot = state.get_attestation_slot(&a.data)?;
     let state_block_root = *state.get_block_root(attestation_slot)?;
diff --git a/eth2/state_processing/src/per_epoch_processing/winning_root.rs b/eth2/state_processing/src/per_epoch_processing/winning_root.rs
index 550e1eaf4..62917a134 100644
--- a/eth2/state_processing/src/per_epoch_processing/winning_root.rs
+++ b/eth2/state_processing/src/per_epoch_processing/winning_root.rs
@@ -47,15 +47,16 @@ pub fn winning_root<T: EthSpec>(
         .filter(|a| a.data.shard == shard)
         .collect();
 
-    let shard_crosslinks = shard_attestations.iter().map(|att| {
-        (
+    let mut shard_crosslinks = Vec::with_capacity(shard_attestations.len());
+    for att in shard_attestations {
+        shard_crosslinks.push((
             att,
-            state.get_crosslink_from_attestation_data(&att.data, spec),
-        )
-    });
+            state.get_crosslink_from_attestation_data(&att.data, spec)?,
+        ));
+    }
 
-    let current_shard_crosslink_root = state.current_crosslinks[shard as usize].tree_hash_root();
-    let candidate_crosslinks = shard_crosslinks.filter(|(_, c)| {
+    let current_shard_crosslink_root = state.get_current_crosslink(shard)?.tree_hash_root();
+    let candidate_crosslinks = shard_crosslinks.into_iter().filter(|(_, c)| {
         c.previous_crosslink_root.as_bytes() == &current_shard_crosslink_root[..]
             || c.tree_hash_root() == current_shard_crosslink_root
     });
@@ -63,7 +64,7 @@ pub fn winning_root<T: EthSpec>(
     // Build a map from candidate crosslink to attestations that support that crosslink.
     let mut candidate_crosslink_map: HashMap<Crosslink, Vec<&PendingAttestation>> = HashMap::new();
 
-    for (&attestation, crosslink) in candidate_crosslinks {
+    for (attestation, crosslink) in candidate_crosslinks {
         let supporting_attestations = candidate_crosslink_map
             .entry(crosslink)
             .or_insert_with(Vec::new);