diff --git a/src/turnbull.rs b/src/turnbull.rs
index 71aa40c..cf7b7bf 100644
--- a/src/turnbull.rs
+++ b/src/turnbull.rs
@@ -56,6 +56,10 @@ pub struct TurnbullArgs {
 	/// Threshold for dropping failure probability in --se-method oim-drop-zeros
 	#[arg(long, default_value="0.0001")]
 	zero_tolerance: f64,
+	
+	/// Desired precision of confidence limits in --se-method likelihood-ratio
+	#[arg(long, default_value="0.01")]
+	ci_precision: f64,
 }
 
 #[derive(ValueEnum, Clone)]
@@ -78,7 +82,7 @@ pub fn main(args: TurnbullArgs) {
 	
 	// Fit regression
 	let progress_bar = ProgressBar::with_draw_target(Some(0), ProgressDrawTarget::term_like(Box::new(UnconditionalTermLike::stderr())));
-	let result = fit_turnbull(data_times, progress_bar, args.max_iterations, args.ll_tolerance, args.se_method, args.zero_tolerance);
+	let result = fit_turnbull(data_times, progress_bar, args.max_iterations, args.ll_tolerance, args.se_method, args.zero_tolerance, args.ci_precision);
 	
 	// Display output
 	match args.output {
@@ -184,7 +188,7 @@ struct Constraint {
 	survival_prob: f64,
 }
 
-pub fn fit_turnbull(data_times: Matrix2xX<f64>, progress_bar: ProgressBar, max_iterations: u32, ll_tolerance: f64, se_method: SEMethod, zero_tolerance: f64) -> TurnbullResult {
+pub fn fit_turnbull(data_times: Matrix2xX<f64>, progress_bar: ProgressBar, max_iterations: u32, ll_tolerance: f64, se_method: SEMethod, zero_tolerance: f64, ci_precision: f64) -> TurnbullResult {
 	// ----------------------
 	// Prepare for regression
 	
@@ -245,7 +249,7 @@ pub fn fit_turnbull(data_times: Matrix2xX<f64>, progress_bar: ProgressBar, max_i
 			progress_bar.println("Computing confidence intervals by likelihood ratio test");
 			
 			let confidence_intervals = (1..data.num_intervals()).into_par_iter()
-				.map(|j| survival_prob_likelihood_ratio_ci(&data, ProgressBar::hidden(), max_iterations, ll_tolerance, &p, ll, &s, &oim_se, j))
+				.map(|j| survival_prob_likelihood_ratio_ci(&data, ProgressBar::hidden(), max_iterations, ll_tolerance, ci_precision, &p, ll, &s, &oim_se, j))
 				.progress_with(progress_bar.clone())
 				.collect();
 			
@@ -607,7 +611,7 @@ fn compute_hessian(data: &TurnbullData, p: &Vec<f64>) -> DMatrix<f64> {
 	return hessian;
 }
 
-fn survival_prob_likelihood_ratio_ci(data: &TurnbullData, progress_bar: ProgressBar, max_iterations: u32, ll_tolerance: f64, p: &Vec<f64>, ll_model: f64, s: &Vec<f64>, oim_se: &Vec<f64>, time_index: usize) -> (f64, f64) {
+fn survival_prob_likelihood_ratio_ci(data: &TurnbullData, progress_bar: ProgressBar, max_iterations: u32, ll_tolerance: f64, ci_precision: f64, p: &Vec<f64>, ll_model: f64, s: &Vec<f64>, oim_se: &Vec<f64>, time_index: usize) -> (f64, f64) {
 	// Compute lower confidence limit
 	let mut ci_bound_lower = 0.0;
 	let mut ci_bound_upper = s[time_index];
@@ -627,10 +631,7 @@ fn survival_prob_likelihood_ratio_ci(data: &TurnbullData, progress_bar: Progress
 		let (_p, ll_test) = fit_turnbull_estimator(data, progress_bar.clone(), max_iterations, ll_tolerance, p_test, Some(Constraint { time_index: time_index, survival_prob: ci_estimate }));
 		let lr_statistic = 2.0 * (ll_model - ll_test);
 		
-		if (lr_statistic - CHI2_1DF_95).abs() < ll_tolerance {
-			// Converged!
-			break;
-		} else if lr_statistic > CHI2_1DF_95 {
+		if lr_statistic > CHI2_1DF_95 {
 			// CI is too wide
 			ci_bound_lower = ci_estimate;
 		} else {
@@ -638,11 +639,13 @@ fn survival_prob_likelihood_ratio_ci(data: &TurnbullData, progress_bar: Progress
 			ci_bound_upper = ci_estimate;
 		}
 		
-		// FIXME: Sometimes this does not converge within max_iterations - investigate why this is
-		// If it is not an issue with the algorithm, then we should also terminate if width of interval is narrower than a specified tolerance
-		
 		ci_estimate = (ci_bound_lower + ci_bound_upper) / 2.0;
 		
+		if ci_bound_upper - ci_bound_lower <= ci_precision {
+			// Desired precision has been reached
+			break;
+		}
+		
 		iteration += 1;
 		if iteration > max_iterations {
 			panic!("Exceeded --max-iterations");
@@ -670,10 +673,7 @@ fn survival_prob_likelihood_ratio_ci(data: &TurnbullData, progress_bar: Progress
 		let (_p, ll_test) = fit_turnbull_estimator(data, progress_bar.clone(), max_iterations, ll_tolerance, p_test, Some(Constraint { time_index: time_index, survival_prob: ci_estimate }));
 		let lr_statistic = 2.0 * (ll_model - ll_test);
 		
-		if (lr_statistic - CHI2_1DF_95).abs() < ll_tolerance {
-			// Converged!
-			break;
-		} else if lr_statistic > CHI2_1DF_95 {
+		if lr_statistic > CHI2_1DF_95 {
 			// CI is too wide
 			ci_bound_upper = ci_estimate;
 		} else {
@@ -683,6 +683,11 @@ fn survival_prob_likelihood_ratio_ci(data: &TurnbullData, progress_bar: Progress
 		
 		ci_estimate = (ci_bound_lower + ci_bound_upper) / 2.0;
 		
+		if ci_bound_upper - ci_bound_lower <= ci_precision {
+			// Desired precision has been reached
+			break;
+		}
+		
 		iteration += 1;
 		if iteration > max_iterations {
 			panic!("Exceeded --max-iterations");