diff --git a/src/Main.cc b/src/Main.cc
index 520eb684..49b6ed87 100644
--- a/src/Main.cc
+++ b/src/Main.cc
@@ -424,6 +424,51 @@ Action a_disassemble_bc0(
       bc0_disassemble(stdout, read_input_data(args));
     });
 
+Action a_psov2_encrypt_single_test(
+    "psov2-encrypt-single-test", nullptr,
+    [](phosg::Arguments& args) {
+      size_t num_threads = args.get<size_t>("threads", std::thread::hardware_concurrency());
+
+      vector<uint64_t> crypt_times(num_threads, 0);
+      vector<uint64_t> single_times(num_threads, 0);
+      uint64_t num_mismatches = 0;
+      mutex output_lock;
+      auto thread_fn = [&](uint64_t seed, size_t thread_index) -> bool {
+        uint64_t start_t = phosg::now();
+        uint32_t crypt_v = PSOV2Encryption(seed).next();
+        uint64_t mid_t = phosg::now();
+        uint32_t single_v = PSOV2Encryption::single(seed);
+        uint64_t end_t = phosg::now();
+
+        crypt_times[thread_index] += (mid_t - start_t);
+        single_times[thread_index] += (end_t - mid_t);
+
+        if (crypt_v != single_v) {
+          lock_guard g(output_lock);
+          phosg::fwrite_fmt(stderr, "Mismatched result on seed {:08X}: crypt={:08X}, single={:08X}\n",
+              seed, crypt_v, single_v);
+          num_mismatches++;
+        }
+        return false;
+      };
+      auto progress_fn = [&](uint64_t, uint64_t, uint64_t current_value, uint64_t) -> void {
+        uint64_t crypt_time = 0, single_time = 0;
+        for (uint64_t t : crypt_times) {
+          crypt_time += t;
+        }
+        for (uint64_t t : single_times) {
+          single_time += t;
+        }
+        lock_guard g(output_lock);
+        phosg::log_info_f("... {:08X} => {} mismatches, {} crypt, {} single ({:g}x)",
+            current_value, num_mismatches, phosg::format_duration(crypt_time), phosg::format_duration(single_time),
+            static_cast<float>(crypt_time) / single_time);
+      };
+      phosg::parallel_range_blocks<uint64_t>(thread_fn, 0, 0x100000000, 0x1000, num_threads, progress_fn);
+
+      progress_fn(0, 0, 0xFFFFFFFF, 0);
+    });
+
 static void a_encrypt_decrypt_fn(phosg::Arguments& args) {
   bool is_decrypt = (args.get<string>(0) == "decrypt-data");
   string seed = args.get<string>("seed");
diff --git a/src/Map.cc b/src/Map.cc
index ccff1f79..715bd294 100644
--- a/src/Map.cc
+++ b/src/Map.cc
@@ -6163,10 +6163,7 @@ void MapState::index_super_map(const FloorConfig& fc, shared_ptr<RandomGenerator
           try {
             det = det_cache.at(seed);
           } catch (const out_of_range&) {
-            // TODO: We only need the first value from this crypt, so it's unfortunate that we have to initialize the
-            // entire thing. Find a way to make this faster.
-            PSOV2Encryption crypt(seed);
-            det = (static_cast<float>((crypt.next() >> 16) & 0xFFFF) / 65536.0f);
+            det = (static_cast<float>((PSOV2Encryption::single(seed) >> 16) & 0xFFFF) / 65536.0f);
             det_cache.emplace(seed, det);
           }
 
diff --git a/src/PSOEncryption.cc b/src/PSOEncryption.cc
index f2b71d3f..14d76530 100644
--- a/src/PSOEncryption.cc
+++ b/src/PSOEncryption.cc
@@ -103,6 +103,32 @@ PSOEncryption::Type PSOV2Encryption::type() const {
   return Type::V2;
 }
 
+uint32_t PSOV2Encryption::single(uint32_t seed) {
+  // This function is an optimized implementation of `PSOV2Encryption(seed).next()`; that is, it allows the caller to
+  // get a single value from a PSOV2Encryption instance without actually constructing it. This method is 22x-100x
+  // faster (depending on build configuration) than constructing a PSOV2Encryption and calling .next() on it once.
+
+  // If fib(n) is the n'th Fibonacci number (starting with 1, 1, 2, 3, 5, etc.), then a closed form for the integer
+  // sequence generated by the first loop in PSOV2Encryption::PSOV2Encryption is:
+  //   a(n) = (-1)^n * (fib(n) - fib(n-1) * seed)
+  // The recurrence used in that loop is a(n) = a(n-2) - a(n-1), which we can use to prove the closed form correct:
+  //   a(n) = a(n-2) - a(n-1)
+  //   a(n) = (-1)^(n-2) * (fib(n-2) - fib(n-3) * seed) - ((-1)^(n-1) * (fib(n-1) - fib(n-2) * seed))
+  //   a(n) = (-1)^(n-2) * (fib(n-2) - fib(n-3) * seed) + ((-1)^(n-2) * (fib(n-1) - fib(n-2) * seed))
+  //   a(n) = (-1)^(n-2) * (fib(n-2) - fib(n-3) * seed + fib(n-1) - fib(n-2) * seed)
+  //   a(n) = (-1)^(n-2) * (fib(n-2) + fib(n-1) - (fib(n-3) + fib(n-2)) * seed)
+  //   a(n) = (-1)^(n-2) * (fib(n) - fib(n-1) * seed)
+  //   a(n) = (-1)^(n) * (fib(n) - fib(n-1) * seed)
+  // The sequence begins with a(-1) = seed (which is not generated by the loop but is used as an initial input, hence
+  // the negative index) and a(0) = 1. Using the closed form and the values of a(-1) and a(0), we can eliminate all
+  // arithmetic done in the normal constructor that isn't necessary to produce the first result value. To do so, we
+  // trace backward from the result value, through the 5 update_stream calls and the initialization loop, to see which
+  // indexes within the stream are actually needed, and the expression to generate each one. We can then simplify the
+  // overall expression and truncate constants to 32 bits (since it's a linear equation, overflow bits cannot affect
+  // the final 32-bit result). The full expression simplifies to:
+  return 0xC6DCAB76 * seed - 0x9E1977BA;
+}
+
 PSOV3Encryption::PSOV3Encryption(uint32_t seed) : PSOLFGEncryption(seed, STREAM_LENGTH, STREAM_LENGTH) {
   uint32_t x, y, basekey, source1, source2, source3;
   basekey = 0;
diff --git a/src/PSOEncryption.hh b/src/PSOEncryption.hh
index ecbdf0db..05b9a939 100644
--- a/src/PSOEncryption.hh
+++ b/src/PSOEncryption.hh
@@ -132,6 +132,9 @@ public:
   explicit PSOV2Encryption(uint32_t seed);
   virtual Type type() const;
 
+  // Optimized implementation of `PSOV2Encryption(seed).next()` for when the caller needs only the first value
+  static uint32_t single(uint32_t seed);
+
 protected:
   virtual void update_stream();