diff --git a/Cargo.lock b/Cargo.lock
index 541d4313c..57f9dd235 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1892,6 +1892,13 @@ dependencies = [
  "rand_core 0.3.1 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
 
+[[package]]
+name = "rangeset"
+version = "0.1.0"
+dependencies = [
+ "num 0.2.0 (registry+https://github.com/rust-lang/crates.io-index)",
+]
+
 [[package]]
 name = "ratelimit_meter"
 version = "5.0.0"
@@ -2792,6 +2799,7 @@ dependencies = [
  "portable-pty 0.2.0",
  "pretty_env_logger 0.3.1 (registry+https://github.com/rust-lang/crates.io-index)",
  "promise 0.2.0",
+ "rangeset 0.1.0",
  "ratelimit_meter 5.0.0 (registry+https://github.com/rust-lang/crates.io-index)",
  "serde 1.0.104 (registry+https://github.com/rust-lang/crates.io-index)",
  "serial 0.4.0 (registry+https://github.com/rust-lang/crates.io-index)",
diff --git a/Cargo.toml b/Cargo.toml
index 971fe7dcf..4302aa89d 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -17,6 +17,7 @@ anyhow = "1.0"
 thiserror = "1.0"
 base64 = "0.10"
 base91 = { path = "base91" }
+rangeset = { path = "rangeset" }
 bitflags = "1.0"
 crossbeam-channel = "0.3"
 dirs = "1.0"
diff --git a/rangeset/Cargo.toml b/rangeset/Cargo.toml
new file mode 100644
index 000000000..9f3523058
--- /dev/null
+++ b/rangeset/Cargo.toml
@@ -0,0 +1,8 @@
+[package]
+name = "rangeset"
+version = "0.1.0"
+authors = ["Wez Furlong <wez@wezfurlong.org>"]
+edition = "2018"
+
+[dependencies]
+num = "0.2"
diff --git a/rangeset/src/lib.rs b/rangeset/src/lib.rs
new file mode 100644
index 000000000..67f481105
--- /dev/null
+++ b/rangeset/src/lib.rs
@@ -0,0 +1,322 @@
+use num::Integer;
+use std::cmp::{max, min};
+use std::fmt::Debug;
+use std::ops::Range;
+
+/// Track a set of integers, collapsing adjacent integers into ranges.
+/// Internally stores the set in an array of ranges.
+/// Allows adding and subtracting ranges.
+#[derive(Debug, Clone, PartialEq)]
+pub struct RangeSet<T: Integer + Copy> {
+    ranges: Vec<Range<T>>,
+}
+
+fn range_is_empty<T: Integer>(range: &Range<T>) -> bool {
+    range.start == range.end
+}
+
+/// Returns true if r1 intersects r2
+fn intersects_range<T: Integer + Copy + Debug>(r1: &Range<T>, r2: &Range<T>) -> bool {
+    let start = max(r1.start, r2.start);
+    let end = min(r1.end, r2.end);
+
+    end > start
+}
+
+#[allow(dead_code)]
+/// Computes the intersection of r1 and r2
+fn range_intersection<T: Integer + Copy + Debug>(r1: &Range<T>, r2: &Range<T>) -> Option<Range<T>> {
+    let start = max(r1.start, r2.start);
+    let end = min(r1.end, r2.end);
+
+    if end > start {
+        Some(start..end)
+    } else {
+        None
+    }
+}
+
+/// Computes the r1 - r2, which may result in up to two non-overlapping ranges.
+fn range_subtract<T: Integer + Copy + Debug>(
+    r1: &Range<T>,
+    r2: &Range<T>,
+) -> (Option<Range<T>>, Option<Range<T>>) {
+    let i_start = max(r1.start, r2.start);
+    let i_end = min(r1.end, r2.end);
+
+    if i_end > i_start {
+        let a = if i_start == r1.start {
+            // Intersection overlaps with the LHS
+            None
+        } else {
+            // The LHS up to the intersection
+            Some(r1.start..r1.end.min(i_start))
+        };
+
+        let b = if i_end == r1.end {
+            // Intersection overlaps with the RHS
+            None
+        } else {
+            // The intersection up to the RHS
+            Some(r1.end.min(i_end)..r1.end)
+        };
+
+        (a, b)
+    } else {
+        // No intersection, so we're left with r1 with nothing removed
+        (Some(r1.clone()), None)
+    }
+}
+
+/// Merge two ranges to produce their union
+fn range_union<T: Integer>(r1: Range<T>, r2: Range<T>) -> Range<T> {
+    let start = r1.start.min(r2.start);
+    let end = r1.end.max(r2.end);
+    start..end
+}
+
+impl<T: Integer + Copy + Debug> RangeSet<T> {
+    /// Create a new set
+    pub fn new() -> Self {
+        Self { ranges: vec![] }
+    }
+
+    /// Returns true if this set is empty
+    pub fn is_empty(&self) -> bool {
+        self.ranges.is_empty()
+    }
+
+    /// Returns true if this set contains the specified integer
+    pub fn contains(&self, value: T) -> bool {
+        for r in &self.ranges {
+            if r.contains(&value) {
+                return true;
+            }
+        }
+        false
+    }
+
+    /// Returns a rangeset containing all of the integers that are present
+    /// in self but not in other.
+    /// The current implementation is `O(n**2)` but this should be "OK"
+    /// as the likely scenario is that there will be a large contiguous
+    /// range for the scrollback, and a smaller contiguous range for changes
+    /// in the viewport.
+    /// If that doesn't hold up, we can improve this.
+    pub fn difference(&self, other: &Self) -> Self {
+        let mut result = Self::new();
+
+        for my_range in &self.ranges {
+            for other_range in &other.ranges {
+                match range_subtract(my_range, other_range) {
+                    (Some(a), Some(b)) => {
+                        result.add_range(a);
+                        result.add_range(b);
+                    }
+                    (Some(a), None) | (None, Some(a)) if a != *other_range => {
+                        result.add_range(a);
+                    }
+                    _ => {}
+                }
+            }
+        }
+
+        result
+    }
+
+    /// Remove a single integer from the set
+    pub fn remove(&mut self, value: T) {
+        self.remove_range(value..value + num::one());
+    }
+
+    /// Remove a range of integers from the set
+    pub fn remove_range(&mut self, range: Range<T>) {
+        let mut to_add = vec![];
+        let mut to_remove = vec![];
+
+        for (idx, r) in self.ranges.iter().enumerate() {
+            match range_subtract(r, &range) {
+                (None, None) => to_remove.push(idx),
+                (Some(a), Some(b)) => {
+                    to_remove.push(idx);
+                    to_add.push(a);
+                    to_add.push(b);
+                }
+                (Some(a), None) | (None, Some(a)) if a != *r => {
+                    to_remove.push(idx);
+                    to_add.push(a);
+                }
+                _ => {}
+            }
+        }
+
+        for idx in to_remove.into_iter().rev() {
+            self.ranges.remove(idx);
+        }
+
+        for r in to_add {
+            self.add_range(r);
+        }
+    }
+
+    /// Remove a set of ranges from this set
+    pub fn remove_set(&mut self, set: &Self) {
+        for r in set.iter() {
+            self.remove_range(r.clone());
+        }
+    }
+
+    /// Add a single integer to the set
+    pub fn add(&mut self, value: T) {
+        self.add_range(value..value + num::one());
+    }
+
+    /// Add a range of integers to the set
+    pub fn add_range(&mut self, range: Range<T>) {
+        if range_is_empty(&range) {
+            return;
+        }
+
+        if self.ranges.is_empty() {
+            self.ranges.push(range.clone());
+            return;
+        }
+
+        match self.intersection_helper(&range) {
+            (Some(a), Some(b)) if b == a + 1 => {
+                // This range intersects with two or more adjacent ranges and will
+                // therefore join them together
+
+                let second = self.ranges[b].clone();
+                let merged = range_union(range, second);
+
+                self.ranges.remove(b);
+                return self.add_range(merged);
+            }
+            (Some(a), _) => self.merge_into_range(a, range),
+            (None, Some(_)) => unreachable!(),
+            (None, None) => {
+                // No intersection, so find the insertion point
+                let idx = self.insertion_point(&range);
+                self.ranges.insert(idx, range.clone());
+            }
+        }
+    }
+
+    /// Add a set of ranges to this set
+    pub fn add_set(&mut self, set: &Self) {
+        for r in set.iter() {
+            self.add_range(r.clone());
+        }
+    }
+
+    fn merge_into_range(&mut self, idx: usize, range: Range<T>) {
+        let existing = self.ranges[idx].clone();
+        self.ranges[idx] = range_union(existing, range);
+    }
+
+    fn intersection_helper(&self, range: &Range<T>) -> (Option<usize>, Option<usize>) {
+        let mut first = None;
+
+        for (idx, r) in self.ranges.iter().enumerate() {
+            if intersects_range(r, range) || r.end == range.start {
+                if first.is_some() {
+                    return (first, Some(idx));
+                }
+                first = Some(idx);
+            }
+        }
+
+        (first, None)
+    }
+
+    fn insertion_point(&self, range: &Range<T>) -> usize {
+        for (idx, r) in self.ranges.iter().enumerate() {
+            if range.end < r.start {
+                return idx;
+            }
+        }
+
+        self.ranges.len()
+    }
+
+    /// Returns an iterator over the ranges that comprise the set
+    pub fn iter(&self) -> impl Iterator<Item = &Range<T>> {
+        self.ranges.iter()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn collect<T: Integer + Copy + Debug>(set: &RangeSet<T>) -> Vec<Range<T>> {
+        set.iter().cloned().collect()
+    }
+
+    #[test]
+    fn add_range() {
+        let mut set = RangeSet::new();
+        set.add(1);
+        set.add(2);
+        set.add(4);
+        assert_eq!(collect(&set), vec![1..3, 4..5]);
+
+        set.add_range(2..6);
+        assert_eq!(collect(&set), vec![1..6]);
+    }
+
+    #[test]
+    fn remove_range() {
+        let mut set = RangeSet::new();
+        set.add_range(1..5);
+        set.add_range(8..10);
+        assert_eq!(collect(&set), vec![1..5, 8..10]);
+
+        // Middle
+        set.remove(2);
+        assert_eq!(collect(&set), vec![1..2, 3..5, 8..10]);
+
+        // RHS
+        set.remove_range(4..7);
+        assert_eq!(collect(&set), vec![1..2, 3..4, 8..10]);
+
+        // Complete overlap of one range, LHS overlap with another
+        set.remove_range(3..9);
+        assert_eq!(collect(&set), vec![1..2, 9..10]);
+    }
+
+    #[test]
+    fn difference() {
+        let mut set = RangeSet::new();
+        set.add_range(1..10);
+
+        let mut other = RangeSet::new();
+        other.add_range(1..15);
+
+        let diff = other.difference(&set);
+        assert_eq!(collect(&diff), vec![10..15]);
+
+        let diff = set.difference(&other);
+        assert_eq!(collect(&diff), vec![]);
+    }
+
+    #[test]
+    fn difference_more() {
+        let mut set = RangeSet::new();
+        set.add(1);
+        set.add(3);
+        set.add(5);
+
+        let mut other = RangeSet::new();
+        other.add(2);
+        other.add(4);
+        other.add(6);
+
+        let diff = other.difference(&set);
+        assert_eq!(collect(&diff), vec![2..3, 4..5, 6..7]);
+
+        let diff = set.difference(&other);
+        assert_eq!(collect(&diff), vec![1..2, 3..4, 5..6]);
+    }
+}