diff --git a/evm_arithmetization/src/generation/mod.rs b/evm_arithmetization/src/generation/mod.rs
index 0ff4f1a00..634e47f63 100644
--- a/evm_arithmetization/src/generation/mod.rs
+++ b/evm_arithmetization/src/generation/mod.rs
@@ -24,7 +24,8 @@ use crate::cpu::kernel::aggregator::KERNEL;
 use crate::cpu::kernel::constants::global_metadata::GlobalMetadata;
 use crate::generation::state::{GenerationState, State};
 use crate::generation::trie_extractor::{get_receipt_trie, get_state_trie, get_txn_trie};
-use crate::memory::segments::Segment;
+use crate::memory::columns::PREINITIALIZED_SEGMENTS;
+use crate::memory::segments::{Segment, PREINITIALIZED_SEGMENTS_INDICES};
 use crate::proof::{
     BlockHashes, BlockMetadata, ExtraBlockData, MemCap, PublicValues, RegistersData, TrieRoots,
 };
@@ -380,20 +381,24 @@ fn initialize_kernel_code_and_shift_table(memory: &mut MemoryState) {
 
 /// Returns the memory addresses and values that should comprise the state at
 /// the start of the segment's execution.
+/// Ignores zero values in non-preinitialized segments.
 fn get_all_memory_address_and_values(memory_before: &MemoryState) -> Vec<(MemoryAddress, U256)> {
     let mut res = vec![];
     for (ctx_idx, ctx) in memory_before.contexts.iter().enumerate() {
         for (segment_idx, segment) in ctx.segments.iter().enumerate() {
             for (virt, value) in segment.content.iter().enumerate() {
                 if let &Some(val) = value {
-                    res.push((
-                        MemoryAddress {
-                            context: ctx_idx,
-                            segment: segment_idx,
-                            virt,
-                        },
-                        val,
-                    ));
+                    // We skip zero values in non-preinitialized segments.
+                    if !val.is_zero() || PREINITIALIZED_SEGMENTS_INDICES.contains(&segment_idx) {
+                        res.push((
+                            MemoryAddress {
+                                context: ctx_idx,
+                                segment: segment_idx,
+                                virt,
+                            },
+                            val,
+                        ));
+                    }
                 }
             }
         }
diff --git a/evm_arithmetization/src/memory/columns.rs b/evm_arithmetization/src/memory/columns.rs
index 459554ea4..626952251 100644
--- a/evm_arithmetization/src/memory/columns.rs
+++ b/evm_arithmetization/src/memory/columns.rs
@@ -67,8 +67,13 @@ pub(crate) const STALE_CONTEXTS_FREQUENCIES: usize = IS_PRUNED + 1;
 // `ADDR_CONTEXT` + 1 is in `STALE_CONTEXTS`.
 pub(crate) const IS_STALE: usize = STALE_CONTEXTS_FREQUENCIES + 1;
 
-// Filter for the `MemAfter` CTL.
-pub(crate) const MEM_AFTER_FILTER: usize = IS_STALE + 1;
+// Flag indicating that a value can potentially be propagated.
+// Contains `filter * address_changed * is_not_stale`.
+pub(crate) const MAYBE_IN_MEM_AFTER: usize = IS_STALE + 1;
+
+// Filter for the `MemAfter` CTL. Is equal to `MAYBE_IN_MEM_AFTER` if segment is
+// preinitialized or the value is non-zero, is 0 otherwise.
+pub(crate) const MEM_AFTER_FILTER: usize = MAYBE_IN_MEM_AFTER + 1;
 
 // We use a range check to enforce the ordering.
 pub(crate) const RANGE_CHECK: usize = MEM_AFTER_FILTER + 1;
diff --git a/evm_arithmetization/src/memory/memory_stark.rs b/evm_arithmetization/src/memory/memory_stark.rs
index 21f57cb2c..4645599a0 100644
--- a/evm_arithmetization/src/memory/memory_stark.rs
+++ b/evm_arithmetization/src/memory/memory_stark.rs
@@ -20,15 +20,16 @@ use starky::lookup::{Column, Filter, Lookup};
 use starky::stark::Stark;
 
 use super::columns::{
-    MEM_AFTER_FILTER, PREINITIALIZED_SEGMENTS, PREINITIALIZED_SEGMENTS_AUX, STALE_CONTEXTS,
+    MAYBE_IN_MEM_AFTER, MEM_AFTER_FILTER, PREINITIALIZED_SEGMENTS, STALE_CONTEXTS,
     STALE_CONTEXTS_FREQUENCIES,
 };
-use super::segments::Segment;
+use super::segments::{Segment, PREINITIALIZED_SEGMENTS_INDICES};
 use crate::all_stark::{EvmStarkFrame, Table};
 use crate::memory::columns::{
     value_limb, ADDR_CONTEXT, ADDR_SEGMENT, ADDR_VIRTUAL, CONTEXT_FIRST_CHANGE, COUNTER, FILTER,
-    FREQUENCIES, INITIALIZE_AUX, IS_PRUNED, IS_READ, IS_STALE, NUM_COLUMNS, RANGE_CHECK,
-    SEGMENT_FIRST_CHANGE, TIMESTAMP, TIMESTAMP_INV, VIRTUAL_FIRST_CHANGE,
+    FREQUENCIES, INITIALIZE_AUX, IS_PRUNED, IS_READ, IS_STALE, NUM_COLUMNS,
+    PREINITIALIZED_SEGMENTS_AUX, RANGE_CHECK, SEGMENT_FIRST_CHANGE, TIMESTAMP, TIMESTAMP_INV,
+    VIRTUAL_FIRST_CHANGE,
 };
 use crate::memory::VALUE_LIMBS;
 use crate::witness::memory::MemoryOpKind::{self, Read};
@@ -42,7 +43,7 @@ use crate::witness::memory::{MemoryAddress, MemoryOp};
 pub(crate) fn ctl_data<F: Field>() -> Vec<Column<F>> {
     let mut res =
         Column::singles([IS_READ, ADDR_CONTEXT, ADDR_SEGMENT, ADDR_VIRTUAL]).collect_vec();
-    res.extend(Column::singles((0..8).map(value_limb)));
+    res.extend(Column::singles((0..VALUE_LIMBS).map(value_limb)));
     res.push(Column::single(TIMESTAMP));
     res
 }
@@ -57,7 +58,7 @@ pub(crate) fn ctl_filter<F: Field>() -> Filter<F> {
 /// - the value in u32 limbs.
 pub(crate) fn ctl_looking_mem<F: Field>() -> Vec<Column<F>> {
     let mut res = Column::singles([ADDR_CONTEXT, ADDR_SEGMENT, ADDR_VIRTUAL]).collect_vec();
-    res.extend(Column::singles((0..8).map(value_limb)));
+    res.extend(Column::singles((0..VALUE_LIMBS).map(value_limb)));
     res
 }
 
@@ -108,11 +109,7 @@ impl MemoryOp {
         let mut row = [F::ZERO; NUM_COLUMNS];
         row[FILTER] = F::from_bool(self.filter);
         row[TIMESTAMP] = F::from_canonical_usize(self.timestamp);
-        if self.timestamp != 0 {
-            row[TIMESTAMP_INV] = row[TIMESTAMP].inverse();
-        } else {
-            row[TIMESTAMP_INV] = F::ZERO;
-        }
+        row[TIMESTAMP_INV] = row[TIMESTAMP].try_inverse().unwrap_or_default();
         row[IS_READ] = F::from_bool(self.kind == Read);
         let MemoryAddress {
             context,
@@ -231,8 +228,8 @@ impl<F: RichField + Extendable<D>, const D: usize> MemoryStark<F, D> {
 
     /// Generates the `COUNTER`, `RANGE_CHECK` and `FREQUENCIES` columns, given
     /// a trace in column-major form.
-    /// Also generates the `STALE_CONTEXTS`, `STALE_CONTEXTS_FREQUENCIES` and
-    /// `MEM_AFTER_FILTER` columns.
+    /// Also generates the `STALE_CONTEXTS`, `STALE_CONTEXTS_FREQUENCIES`,
+    /// `MAYBE_IN_MEM_AFTER` and `MEM_AFTER_FILTER` columns.
     fn generate_trace_col_major(trace_col_vecs: &mut [Vec<F>]) {
         let height = trace_col_vecs[0].len();
         trace_col_vecs[COUNTER] = (0..height).map(|i| F::from_canonical_usize(i)).collect();
@@ -261,8 +258,19 @@ impl<F: RichField + Extendable<D>, const D: usize> MemoryStark<F, D> {
                     || trace_col_vecs[SEGMENT_FIRST_CHANGE][i].is_one()
                     || trace_col_vecs[VIRTUAL_FIRST_CHANGE][i].is_one())
             {
-                // `mem_after_filter = filter * address_changed * (1 - is_stale)`
-                trace_col_vecs[MEM_AFTER_FILTER][i] = F::ONE;
+                // `maybe_in_mem_after = filter * address_changed * (1 - is_stale)`
+                trace_col_vecs[MAYBE_IN_MEM_AFTER][i] = F::ONE;
+
+                let addr_segment = trace_col_vecs[ADDR_SEGMENT][i];
+                let is_non_zero_value =
+                    (0..VALUE_LIMBS).any(|limb| trace_col_vecs[value_limb(limb)][i].is_nonzero());
+                // We filter out zero values in non-preinitialized segments.
+                if is_non_zero_value
+                    || PREINITIALIZED_SEGMENTS_INDICES
+                        .contains(&(addr_segment.to_canonical_u64() as usize))
+                {
+                    trace_col_vecs[MEM_AFTER_FILTER][i] = F::ONE;
+                }
             }
         }
     }
@@ -472,14 +480,18 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for MemoryStark<F
         let addr_context = local_values[ADDR_CONTEXT];
         let addr_segment = local_values[ADDR_SEGMENT];
         let addr_virtual = local_values[ADDR_VIRTUAL];
-        let value_limbs: Vec<_> = (0..8).map(|i| local_values[value_limb(i)]).collect();
+        let value_limbs: Vec<_> = (0..VALUE_LIMBS)
+            .map(|i| local_values[value_limb(i)])
+            .collect();
 
         let next_timestamp = next_values[TIMESTAMP];
         let next_is_read = next_values[IS_READ];
         let next_addr_context = next_values[ADDR_CONTEXT];
         let next_addr_segment = next_values[ADDR_SEGMENT];
         let next_addr_virtual = next_values[ADDR_VIRTUAL];
-        let next_values_limbs: Vec<_> = (0..8).map(|i| next_values[value_limb(i)]).collect();
+        let next_values_limbs: Vec<_> = (0..VALUE_LIMBS)
+            .map(|i| next_values[value_limb(i)])
+            .collect();
 
         // The filter must be 0 or 1.
         let filter = local_values[FILTER];
@@ -561,7 +573,7 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for MemoryStark<F
             initialize_aux - preinitialized_segments * not_address_unchanged * next_is_read,
         );
 
-        for i in 0..8 {
+        for i in 0..VALUE_LIMBS {
             // Enumerate purportedly-ordered log.
             yield_constr.constraint_transition(
                 next_is_read * address_unchanged * (next_values_limbs[i] - value_limbs[i]),
@@ -573,14 +585,27 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for MemoryStark<F
             yield_constr.constraint_transition(initialize_aux * next_values_limbs[i]);
         }
 
-        // Validate `mem_after_filter`.
-        let mem_after_filter = local_values[MEM_AFTER_FILTER];
+        // Validate `maybe_in_mem_after`.
+        let maybe_in_mem_after = local_values[MAYBE_IN_MEM_AFTER];
         let is_stale = local_values[IS_STALE];
         yield_constr.constraint_transition(
-            mem_after_filter + filter * not_address_unchanged * (is_stale - P::ONES),
+            maybe_in_mem_after + filter * not_address_unchanged * (is_stale - P::ONES),
         );
 
-        // Validate `timestamp_inv`. Since it's used as a CTL filter, its value must be
+        let mem_after_filter = local_values[MEM_AFTER_FILTER];
+        // `mem_after_filter` must be binary.
+        yield_constr.constraint(mem_after_filter * (mem_after_filter - P::ONES));
+
+        // `mem_after_filter` is equal to `maybe_in_mem_after` if:
+        // - segment is not preinitialized OR
+        // - value is not zero.
+        for i in 0..VALUE_LIMBS {
+            yield_constr.constraint(
+                (mem_after_filter - maybe_in_mem_after) * preinitialized_segments * value_limbs[i],
+            );
+        }
+
+        // Validate timestamp_inv. Since it's used as a CTL filter, its value must be
         // checked.
         let timestamp_inv = local_values[TIMESTAMP_INV];
         yield_constr.constraint(timestamp * (timestamp * timestamp_inv - P::ONES));
@@ -607,13 +632,17 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for MemoryStark<F
         let addr_context = local_values[ADDR_CONTEXT];
         let addr_segment = local_values[ADDR_SEGMENT];
         let addr_virtual = local_values[ADDR_VIRTUAL];
-        let value_limbs: Vec<_> = (0..8).map(|i| local_values[value_limb(i)]).collect();
+        let value_limbs: Vec<_> = (0..VALUE_LIMBS)
+            .map(|i| local_values[value_limb(i)])
+            .collect();
         let timestamp = local_values[TIMESTAMP];
 
         let next_addr_context = next_values[ADDR_CONTEXT];
         let next_addr_segment = next_values[ADDR_SEGMENT];
         let next_addr_virtual = next_values[ADDR_VIRTUAL];
-        let next_values_limbs: Vec<_> = (0..8).map(|i| next_values[value_limb(i)]).collect();
+        let next_values_limbs: Vec<_> = (0..VALUE_LIMBS)
+            .map(|i| next_values[value_limb(i)])
+            .collect();
         let next_is_read = next_values[IS_READ];
         let next_timestamp = next_values[TIMESTAMP];
 
@@ -758,7 +787,7 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for MemoryStark<F
             builder.sub_extension(initialize_aux, computed_initialize_aux);
         yield_constr.constraint_transition(builder, new_first_read_constraint);
 
-        for i in 0..8 {
+        for i in 0..VALUE_LIMBS {
             // Enumerate purportedly-ordered log.
             let value_diff = builder.sub_extension(next_values_limbs[i], value_limbs[i]);
             let zero_if_read = builder.mul_extension(address_unchanged, value_diff);
@@ -772,16 +801,34 @@ impl<F: RichField + Extendable<D>, const D: usize> Stark<F, D> for MemoryStark<F
             yield_constr.constraint_transition(builder, zero_init_constraint);
         }
 
-        // Validate `mem_after_filter`.
-        let mem_after_filter = local_values[MEM_AFTER_FILTER];
+        // Validate `maybe_in_mem_after`.
+        let maybe_in_mem_after = local_values[MAYBE_IN_MEM_AFTER];
         let is_stale = local_values[IS_STALE];
         {
             let rhs = builder.mul_extension(filter, not_address_unchanged);
             let rhs = builder.mul_sub_extension(rhs, is_stale, rhs);
-            let constr = builder.add_extension(mem_after_filter, rhs);
+            let constr = builder.add_extension(maybe_in_mem_after, rhs);
             yield_constr.constraint_transition(builder, constr);
         }
 
+        let mem_after_filter = local_values[MEM_AFTER_FILTER];
+        // `mem_after_filter` must be binary.
+        {
+            let constr =
+                builder.mul_sub_extension(mem_after_filter, mem_after_filter, mem_after_filter);
+            yield_constr.constraint(builder, constr);
+        }
+
+        // `mem_after_filter` is equal to `maybe_in_mem_after` if:
+        // - segment is not preinitialized OR
+        // - value is not zero.
+        let mem_after_filter_diff = builder.sub_extension(mem_after_filter, maybe_in_mem_after);
+        for i in 0..VALUE_LIMBS {
+            let prod = builder.mul_extension(preinitialized_segments, value_limbs[i]);
+            let constr = builder.mul_extension(mem_after_filter_diff, prod);
+            yield_constr.constraint(builder, constr);
+        }
+
         // Validate timestamp_inv. Since it's used as a CTL filter, its value must be
         // checked.
         let timestamp_inv = local_values[TIMESTAMP_INV];
diff --git a/evm_arithmetization/src/memory/segments.rs b/evm_arithmetization/src/memory/segments.rs
index b95f5e7c4..10e06fc19 100644
--- a/evm_arithmetization/src/memory/segments.rs
+++ b/evm_arithmetization/src/memory/segments.rs
@@ -82,6 +82,14 @@ pub(crate) enum Segment {
     StorageLinkedList = 35 << SEGMENT_SCALING_FACTOR,
 }
 
+// These segments are not zero-initialized.
+pub(crate) const PREINITIALIZED_SEGMENTS_INDICES: [usize; 4] = [
+    Segment::Code.unscale(),
+    Segment::TrieData.unscale(),
+    Segment::AccountsLinkedList.unscale(),
+    Segment::StorageLinkedList.unscale(),
+];
+
 impl Segment {
     pub(crate) const COUNT: usize = 36;
 
diff --git a/evm_arithmetization/src/witness/memory.rs b/evm_arithmetization/src/witness/memory.rs
index e69e75f96..1b7d709ba 100644
--- a/evm_arithmetization/src/witness/memory.rs
+++ b/evm_arithmetization/src/witness/memory.rs
@@ -17,7 +17,7 @@ use MemoryChannel::{Code, GeneralPurpose, PartialChannel};
 
 use super::operation::CONTEXT_SCALING_FACTOR;
 use crate::cpu::kernel::constants::global_metadata::GlobalMetadata;
-use crate::memory::segments::{Segment, SEGMENT_SCALING_FACTOR};
+use crate::memory::segments::{Segment, PREINITIALIZED_SEGMENTS_INDICES, SEGMENT_SCALING_FACTOR};
 use crate::witness::errors::MemoryError::{ContextTooLarge, SegmentTooLarge, VirtTooLarge};
 use crate::witness::errors::ProgramError;
 use crate::witness::errors::ProgramError::MemoryError;
@@ -225,11 +225,7 @@ impl MemoryState {
     /// need a specific behaviour here, since the values can be stored either in
     /// `preinitialized_segments` or in the memory itself.
     pub(crate) fn get_preinit_memory(&self, segment: Segment) -> Vec<Option<U256>> {
-        assert!(
-            segment == Segment::AccountsLinkedList
-                || segment == Segment::StorageLinkedList
-                || segment == Segment::TrieData
-        );
+        assert!(PREINITIALIZED_SEGMENTS_INDICES.contains(&segment.unscale()));
         let len = self
             .preinitialized_segments
             .get(&segment)
@@ -301,6 +297,7 @@ impl MemoryState {
         segment: Segment,
         values: MemorySegmentState,
     ) {
+        assert!(PREINITIALIZED_SEGMENTS_INDICES.contains(&segment.unscale()));
         self.preinitialized_segments.insert(segment, values);
     }