diff --git a/mini-lsm-mvcc/src/compact/tiered.rs b/mini-lsm-mvcc/src/compact/tiered.rs
index 57491ce..d268ec2 100644
--- a/mini-lsm-mvcc/src/compact/tiered.rs
+++ b/mini-lsm-mvcc/src/compact/tiered.rs
@@ -16,6 +16,7 @@ pub struct TieredCompactionOptions {
     pub max_size_amplification_percent: usize,
     pub size_ratio: usize,
     pub min_merge_width: usize,
+    pub max_merge_width: Option<usize>,
 }
 
 pub struct TieredCompactionController {
@@ -61,25 +62,29 @@ impl TieredCompactionController {
         for id in 0..(snapshot.levels.len() - 1) {
             size += snapshot.levels[id].1.len();
             let next_level_size = snapshot.levels[id + 1].1.len();
-            let current_size_ratio = size as f64 / next_level_size as f64;
-            if current_size_ratio >= size_ratio_trigger && id + 2 >= self.options.min_merge_width {
+            let current_size_ratio = next_level_size as f64 / size as f64;
+            if current_size_ratio > size_ratio_trigger && id + 1 >= self.options.min_merge_width {
                 println!(
-                    "compaction triggered by size ratio: {}",
-                    current_size_ratio * 100.0
+                    "compaction triggered by size ratio: {} > {}",
+                    current_size_ratio * 100.0,
+                    size_ratio_trigger * 100.0
                 );
                 return Some(TieredCompactionTask {
                     tiers: snapshot
                         .levels
                         .iter()
-                        .take(id + 2)
+                        .take(id + 1)
                         .cloned()
                         .collect::<Vec<_>>(),
-                    bottom_tier_included: id + 2 >= snapshot.levels.len(),
+                    bottom_tier_included: id + 1 >= snapshot.levels.len(),
                 });
             }
         }
         // trying to reduce sorted runs without respecting size ratio
-        let num_tiers_to_take = snapshot.levels.len() - self.options.num_tiers + 2;
+        let num_tiers_to_take = snapshot
+            .levels
+            .len()
+            .min(self.options.max_merge_width.unwrap_or(usize::MAX));
         println!("compaction triggered by reducing sorted runs");
         return Some(TieredCompactionTask {
             tiers: snapshot
diff --git a/mini-lsm-mvcc/src/table/bloom.rs b/mini-lsm-mvcc/src/table/bloom.rs
index ed64901..2fb5622 100644
--- a/mini-lsm-mvcc/src/table/bloom.rs
+++ b/mini-lsm-mvcc/src/table/bloom.rs
@@ -87,7 +87,7 @@ impl Bloom {
         filter.resize(nbytes, 0);
         for h in keys {
             let mut h = *h;
-            let delta = (h >> 17) | (h << 15);
+            let delta = h.rotate_left(15);
             for _ in 0..k {
                 let bit_pos = (h as usize) % nbits;
                 filter.set_bit(bit_pos, true);
@@ -107,7 +107,7 @@ impl Bloom {
             true
         } else {
             let nbits = self.filter.bit_len();
-            let delta = (h >> 17) | (h << 15);
+            let delta = h.rotate_left(15);
             for _ in 0..self.k {
                 let bit_pos = h % (nbits as u32);
                 if !self.filter.get_bit(bit_pos as usize) {
diff --git a/mini-lsm-starter/src/bin/compaction-simulator.rs b/mini-lsm-starter/src/bin/compaction-simulator.rs
index 3d8047b..67f44bc 100644
--- a/mini-lsm-starter/src/bin/compaction-simulator.rs
+++ b/mini-lsm-starter/src/bin/compaction-simulator.rs
@@ -19,8 +19,17 @@ use mini_lsm_wrapper::table::SsTable;
 #[command(author, version, about, long_about = None)]
 enum Args {
     Simple {
+        /// Dump the generated ID instead of where the original data comes from.
+        /// For example, if SST 1, 2, 3 is compacted to another level, it should have
+        /// a new SST ID 4, 5, 6 as SSTs are immutable and write-once. With this flag
+        /// enabled, you will see the new level has SST 1, 2, 3 because the data of
+        /// 4, 5, 6 are originated from 1, 2, 3.
         #[clap(long)]
         dump_real_id: bool,
+        /// Only dump size information instead of the layer files. if this is enabled,
+        /// it will print one row per compaction iteration.
+        #[clap(long)]
+        size_only: bool,
         #[clap(long, default_value = "2")]
         level0_file_num_compaction_trigger: usize,
         #[clap(long, default_value = "3")]
@@ -31,8 +40,17 @@ enum Args {
         iterations: usize,
     },
     Tiered {
+        /// Dump the generated ID instead of where the original data comes from.
+        /// For example, if SST 1, 2, 3 is compacted to another level, it should have
+        /// a new SST ID 4, 5, 6 as SSTs are immutable and write-once. With this flag
+        /// enabled, you will see the new level has SST 1, 2, 3 because the data of
+        /// 4, 5, 6 are originated from 1, 2, 3.
         #[clap(long)]
         dump_real_id: bool,
+        /// Only dump size information instead of the layer files. if this is enabled,
+        /// it will print one row per compaction iteration.
+        #[clap(long)]
+        size_only: bool,
         #[clap(long, default_value = "3")]
         num_tiers: usize,
         #[clap(long, default_value = "200")]
@@ -41,12 +59,23 @@ enum Args {
         size_ratio: usize,
         #[clap(long, default_value = "2")]
         min_merge_width: usize,
+        #[clap(long)]
+        max_merge_width: Option<usize>,
         #[clap(long, default_value = "50")]
         iterations: usize,
     },
     Leveled {
+        /// Dump the generated ID instead of where the original data comes from.
+        /// For example, if SST 1, 2, 3 is compacted to another level, it should have
+        /// a new SST ID 4, 5, 6 as SSTs are immutable and write-once. With this flag
+        /// enabled, you will see the new level has SST 1, 2, 3 because the data of
+        /// 4, 5, 6 are originated from 1, 2, 3.
         #[clap(long)]
         dump_real_id: bool,
+        /// Only dump size information instead of the layer files. if this is enabled,
+        /// it will print one row per compaction iteration.
+        #[clap(long)]
+        size_only: bool,
         #[clap(long, default_value = "2")]
         level0_file_num_compaction_trigger: usize,
         #[clap(long, default_value = "2")]
@@ -148,6 +177,14 @@ impl MockStorage {
         }
     }
 
+    pub fn dump_size_only(&self) {
+        print!("Levels: {}", self.snapshot.l0_sstables.len());
+        for (_, files) in &self.snapshot.levels {
+            print!(" {}", files.len());
+        }
+        println!();
+    }
+
     pub fn dump_original_id(&self, always_show_l0: bool, with_key: bool) {
         if !self.snapshot.l0_sstables.is_empty() || always_show_l0 {
             println!(
@@ -231,6 +268,7 @@ fn main() {
     match args {
         Args::Simple {
             dump_real_id,
+            size_only,
             size_ratio_percent,
             iterations,
             level0_file_num_compaction_trigger,
@@ -252,14 +290,18 @@ fn main() {
                 println!("=== Iteration {i} ===");
                 storage.flush_sst_to_l0();
                 println!("--- After Flush ---");
-                if dump_real_id {
+                if size_only {
+                    storage.dump_size_only();
+                } else if dump_real_id {
                     storage.dump_real_id(true, false);
                 } else {
                     storage.dump_original_id(true, false);
                 }
                 let mut num_compactions = 0;
                 while let Some(task) = {
-                    println!("--- Compaction Task ---");
+                    if !size_only {
+                        println!("--- Compaction Task ---");
+                    }
                     controller.generate_compaction_task(&storage.snapshot)
                 } {
                     let mut sst_ids = Vec::new();
@@ -289,7 +331,9 @@ fn main() {
                     storage.snapshot = snapshot;
                     storage.remove(&del);
                     println!("--- After Compaction ---");
-                    if dump_real_id {
+                    if size_only {
+                        storage.dump_size_only();
+                    } else if dump_real_id {
                         storage.dump_real_id(true, false);
                     } else {
                         storage.dump_original_id(true, false);
@@ -333,10 +377,12 @@ fn main() {
         }
         Args::Tiered {
             dump_real_id,
+            size_only,
             num_tiers: level0_file_num_compaction_trigger,
             max_size_amplification_percent,
             size_ratio,
             min_merge_width,
+            max_merge_width,
             iterations,
         } => {
             let controller = TieredCompactionController::new(TieredCompactionOptions {
@@ -344,6 +390,7 @@ fn main() {
                 max_size_amplification_percent,
                 size_ratio,
                 min_merge_width,
+                max_merge_width,
             });
             let mut storage = MockStorage::new();
             let mut max_space = 0;
@@ -351,15 +398,21 @@ fn main() {
                 println!("=== Iteration {i} ===");
                 storage.flush_sst_to_new_tier();
                 println!("--- After Flush ---");
-                if dump_real_id {
+                if size_only {
+                    storage.dump_size_only();
+                } else if dump_real_id {
                     storage.dump_real_id(false, false);
                 } else {
                     storage.dump_original_id(false, false);
                 }
-                println!("--- Compaction Task ---");
+                if !size_only {
+                    println!("--- Compaction Task ---");
+                }
                 let mut num_compactions = 0;
                 while let Some(task) = {
-                    println!("--- Compaction Task ---");
+                    if !size_only {
+                        println!("--- Compaction Task ---");
+                    }
                     controller.generate_compaction_task(&storage.snapshot)
                 } {
                     let mut sst_ids = Vec::new();
@@ -379,7 +432,9 @@ fn main() {
                     storage.snapshot = snapshot;
                     storage.remove(&del);
                     println!("--- After Compaction ---");
-                    if dump_real_id {
+                    if size_only {
+                        storage.dump_size_only();
+                    } else if dump_real_id {
                         storage.dump_real_id(false, false);
                     } else {
                         storage.dump_original_id(false, false);
@@ -423,6 +478,7 @@ fn main() {
         }
         Args::Leveled {
             dump_real_id,
+            size_only,
             level0_file_num_compaction_trigger,
             level_size_multiplier,
             max_levels,
@@ -456,14 +512,18 @@ fn main() {
                     )),
                 );
                 println!("--- After Flush ---");
-                if dump_real_id {
+                if size_only {
+                    storage.dump_size_only();
+                } else if dump_real_id {
                     storage.dump_real_id(false, true);
                 } else {
                     storage.dump_original_id(false, true);
                 }
                 let mut num_compactions = 0;
                 while let Some(task) = {
-                    println!("--- Compaction Task ---");
+                    if !size_only {
+                        println!("--- Compaction Task ---");
+                    }
                     controller.generate_compaction_task(&storage.snapshot)
                 } {
                     let mut sst_ids = Vec::new();
@@ -570,7 +630,9 @@ fn main() {
                     storage.snapshot = snapshot;
                     storage.remove(&del);
                     println!("--- After Compaction ---");
-                    if dump_real_id {
+                    if size_only {
+                        storage.dump_size_only();
+                    } else if dump_real_id {
                         storage.dump_real_id(true, true);
                     } else {
                         storage.dump_original_id(true, true);
diff --git a/mini-lsm-starter/src/bin/mini-lsm-cli.rs b/mini-lsm-starter/src/bin/mini-lsm-cli.rs
index b2f6595..f01d363 100644
--- a/mini-lsm-starter/src/bin/mini-lsm-cli.rs
+++ b/mini-lsm-starter/src/bin/mini-lsm-cli.rs
@@ -334,6 +334,7 @@ fn main() -> Result<()> {
                     max_size_amplification_percent: 200,
                     size_ratio: 1,
                     min_merge_width: 2,
+                    max_merge_width: None,
                 }),
                 CompactionStrategy::Leveled => {
                     CompactionOptions::Leveled(LeveledCompactionOptions {
diff --git a/mini-lsm-starter/src/compact/tiered.rs b/mini-lsm-starter/src/compact/tiered.rs
index 25f300e..b74edd0 100644
--- a/mini-lsm-starter/src/compact/tiered.rs
+++ b/mini-lsm-starter/src/compact/tiered.rs
@@ -14,6 +14,7 @@ pub struct TieredCompactionOptions {
     pub max_size_amplification_percent: usize,
     pub size_ratio: usize,
     pub min_merge_width: usize,
+    pub max_merge_width: Option<usize>,
 }
 
 pub struct TieredCompactionController {
diff --git a/mini-lsm-starter/src/table/bloom.rs b/mini-lsm-starter/src/table/bloom.rs
index 71dfc5b..239a9e4 100644
--- a/mini-lsm-starter/src/table/bloom.rs
+++ b/mini-lsm-starter/src/table/bloom.rs
@@ -94,7 +94,7 @@ impl Bloom {
             true
         } else {
             let nbits = self.filter.bit_len();
-            let delta = (h >> 17) | (h << 15);
+            let delta = h.rotate_left(15);
 
             // TODO: probe the bloom filter
 
diff --git a/mini-lsm/src/compact/tiered.rs b/mini-lsm/src/compact/tiered.rs
index 57491ce..d268ec2 100644
--- a/mini-lsm/src/compact/tiered.rs
+++ b/mini-lsm/src/compact/tiered.rs
@@ -16,6 +16,7 @@ pub struct TieredCompactionOptions {
     pub max_size_amplification_percent: usize,
     pub size_ratio: usize,
     pub min_merge_width: usize,
+    pub max_merge_width: Option<usize>,
 }
 
 pub struct TieredCompactionController {
@@ -61,25 +62,29 @@ impl TieredCompactionController {
         for id in 0..(snapshot.levels.len() - 1) {
             size += snapshot.levels[id].1.len();
             let next_level_size = snapshot.levels[id + 1].1.len();
-            let current_size_ratio = size as f64 / next_level_size as f64;
-            if current_size_ratio >= size_ratio_trigger && id + 2 >= self.options.min_merge_width {
+            let current_size_ratio = next_level_size as f64 / size as f64;
+            if current_size_ratio > size_ratio_trigger && id + 1 >= self.options.min_merge_width {
                 println!(
-                    "compaction triggered by size ratio: {}",
-                    current_size_ratio * 100.0
+                    "compaction triggered by size ratio: {} > {}",
+                    current_size_ratio * 100.0,
+                    size_ratio_trigger * 100.0
                 );
                 return Some(TieredCompactionTask {
                     tiers: snapshot
                         .levels
                         .iter()
-                        .take(id + 2)
+                        .take(id + 1)
                         .cloned()
                         .collect::<Vec<_>>(),
-                    bottom_tier_included: id + 2 >= snapshot.levels.len(),
+                    bottom_tier_included: id + 1 >= snapshot.levels.len(),
                 });
             }
         }
         // trying to reduce sorted runs without respecting size ratio
-        let num_tiers_to_take = snapshot.levels.len() - self.options.num_tiers + 2;
+        let num_tiers_to_take = snapshot
+            .levels
+            .len()
+            .min(self.options.max_merge_width.unwrap_or(usize::MAX));
         println!("compaction triggered by reducing sorted runs");
         return Some(TieredCompactionTask {
             tiers: snapshot
diff --git a/mini-lsm/src/table/bloom.rs b/mini-lsm/src/table/bloom.rs
index ed64901..2fb5622 100644
--- a/mini-lsm/src/table/bloom.rs
+++ b/mini-lsm/src/table/bloom.rs
@@ -87,7 +87,7 @@ impl Bloom {
         filter.resize(nbytes, 0);
         for h in keys {
             let mut h = *h;
-            let delta = (h >> 17) | (h << 15);
+            let delta = h.rotate_left(15);
             for _ in 0..k {
                 let bit_pos = (h as usize) % nbits;
                 filter.set_bit(bit_pos, true);
@@ -107,7 +107,7 @@ impl Bloom {
             true
         } else {
             let nbits = self.filter.bit_len();
-            let delta = (h >> 17) | (h << 15);
+            let delta = h.rotate_left(15);
             for _ in 0..self.k {
                 let bit_pos = h % (nbits as u32);
                 if !self.filter.get_bit(bit_pos as usize) {
diff --git a/mini-lsm/src/tests/harness.rs b/mini-lsm/src/tests/harness.rs
index b41745b..0553b03 100644
--- a/mini-lsm/src/tests/harness.rs
+++ b/mini-lsm/src/tests/harness.rs
@@ -368,6 +368,7 @@ pub fn check_compaction_ratio(storage: Arc<MiniLsm>) {
             max_size_amplification_percent,
             size_ratio,
             min_merge_width,
+            ..
         }) => {
             let size_ratio_trigger = (100.0 + size_ratio as f64) / 100.0;
             assert_eq!(l0_sst_num, 0);
diff --git a/mini-lsm/src/tests/week2_day3.rs b/mini-lsm/src/tests/week2_day3.rs
index 6e124db..e37d88b 100644
--- a/mini-lsm/src/tests/week2_day3.rs
+++ b/mini-lsm/src/tests/week2_day3.rs
@@ -18,6 +18,7 @@ fn test_integration() {
                 max_size_amplification_percent: 200,
                 size_ratio: 1,
                 min_merge_width: 2,
+                max_merge_width: None,
             },
         )),
     )
diff --git a/mini-lsm/src/tests/week2_day5.rs b/mini-lsm/src/tests/week2_day5.rs
index 5199c76..26e7cdd 100644
--- a/mini-lsm/src/tests/week2_day5.rs
+++ b/mini-lsm/src/tests/week2_day5.rs
@@ -29,6 +29,7 @@ fn test_integration_tiered() {
         max_size_amplification_percent: 200,
         size_ratio: 1,
         min_merge_width: 3,
+        max_merge_width: None,
     }))
 }
 
diff --git a/mini-lsm/src/tests/week2_day6.rs b/mini-lsm/src/tests/week2_day6.rs
index befd100..612f45e 100644
--- a/mini-lsm/src/tests/week2_day6.rs
+++ b/mini-lsm/src/tests/week2_day6.rs
@@ -26,6 +26,7 @@ fn test_integration_tiered() {
         max_size_amplification_percent: 200,
         size_ratio: 1,
         min_merge_width: 3,
+        max_merge_width: None,
     }))
 }